Exhibit 99.1

Leo Holdings Corp. Announces Extraordinary General Meeting Teleconference Details

LONDON, UK, July 6, 2020 — Leo Holdings Corp. (“Leo”) (NYSE: LHC), today announced that, due to the public health and safety concerns related to the coronavirus (COVID-19) pandemic and recommendations and orders from federal and New York authorities, the extraordinary general meeting of Leo’s shareholders, which will be held on Tuesday, July 14, 2020 at 9:00 a.m., New York City Time (the “General Meeting”) will be held remotely by teleconference. The purpose of the General Meeting is to vote on certain proposals relating to the previously announced Business Combination Agreement, dated as of April 23, 2020 (the “Business Combination Agreement”), by and among Leo, Digital Media Solutions LLC (“DMS”) and the other parties thereto.

The General Meeting will be accessible by dialing (833) 780-7941 (toll free—North America) or (469) 333-9522 (International). Shareholders will be able to ask questions to Leo’s management via the conference line.

General Information

All information about the General Meeting, including the definitive proxy statement, is available at https://www.cstproxy.com/leoholdingscorp/2020.

In connection with the transactions contemplated by the Business Combination Agreement (“Business Combination Agreement”), Leo has filed with the U.S. Securities and Exchange Commission’s (“SEC”) a Registration Statement on Form S-4 (the “Registration Statement”) and mailed a definitive proxy statement/prospectus and other relevant documents to its shareholders. This press release is not a substitute for the Registration Statement, the definitive proxy statement/prospectus or any other document that Leo will send to its shareholders in connection with the transactions contemplated by the Business Combination Agreement (the “Business Combination”). Investors and security holders of Leo are advised to read the definitive proxy statement/prospectus in connection with Leo’s solicitation of proxies for its extraordinary general meeting of shareholders to be held to approve the Business Combination (and related matters) because the definitive proxy statement/prospectus contains important information about the Business Combination and the parties to the Business Combination. The definitive proxy statement/prospectus was mailed to shareholders of Leo as of June 24, 2020, the record date established for voting on the Business Combination. Shareholders are also be able to obtain copies of the definitive proxy statement/prospectus, without charge, at the SEC’s website at www.sec.gov or by directing a request to: Leo Holdings Corp., 21 Grosvenor Place, London SW1X 7HF, United Kingdom.

Participants in the Solicitation

Leo and its directors, executive officers, other members of management, and employees, under SEC rules, may be deemed to be participants in the solicitation of proxies of Leo’s shareholders in connection with the Business Combination. Investors and security holders may obtain more detailed information regarding the names and interests in the Business Combination of Leo’s directors and officers in Leo’s filings with the SEC, including Leo’s Annual Report on Form 10-K for the fiscal year ended December 31, 2019, which was filed with the SEC on March 13, 2020, as well as in the Registration Statement, which includes the definitive proxy statement/prospectus of Leo for the Business Combination. Shareholders can obtain copies of Leo’s filings with the SEC, without charge, at the SEC’s website at www.sec.gov.

About Leo Holdings Corp.

Leo is a blank check company formed for the purpose of effecting a merger, share exchange, asset acquisition, share purchase, reorganization or similar business combination with one or more businesses.

About Digital Media Solutions LLC

Digital Media Solutions, LLC (DMS) is a leading provider of technology and digital performance marketing solutions leveraging innovative, performance-driven brand direct and marketplace solutions to connect consumers and advertisers. DMS deploys a robust database of consumer intelligence and leverages massive proprietary media distribution to provide customer acquisition campaigns that grow businesses. Continuing to experience explosive

year-over-year growth, DMS has been continuously recognized on the Inc. 5000 list, securing its sixth consecutive ranking in 2019, and the Entrepreneur magazine 360 list. Named one of America’s “Best Places to Work” by Inc. magazine and awarded the Excellence in Lead Generation Award by the LeadsCouncil, DMS brings together some of the industry’s most knowledgeable people, efficient processes and sophisticated technology across the digital marketing spectrum.

Forward-Looking Statements

This press release includes “forward-looking statements” within the meaning of the “safe harbor” provisions of the Private Securities Litigation Reform Act of 1995. Leo’s and DMS’s actual results may differ from their expectations, estimates and projections and consequently, you should not rely on these forward looking statements as predictions of future events. Words such as “expect,” “estimate,” “project,” “budget,” “forecast,” “anticipate,” “intend,” “plan,” “may,” “will,” “could,” “should,” “believes,” “predicts,” “potential,” “continue,” and similar expressions are intended to identify such forward-looking statements. These forward-looking statements include, without limitation, Leo’s and DMS’s expectations with respect to future performance and anticipated financial impacts of the proposed Business Combination, the satisfaction of the closing conditions to the Business Combination and the timing of the completion of the Business Combination. These forward-looking statements involve significant risks and uncertainties that could cause the actual results to differ materially from the expected results. Most of these factors are outside Leo’s and DMS’s control and are difficult to predict. Factors that may cause such differences include, but are not limited to: (1) the occurrence of any event, change or other circumstances that could give rise to the termination of the Business Combination Agreement; (2) the outcome of any legal proceedings that may be instituted against Leo and DMS following the announcement of the Business Combination Agreement and the transactions contemplated therein; (3) the inability to complete the proposed Business Combination, including due to failure to obtain approval of the shareholders of Leo or other conditions to closing in the Business Combination Agreement; (4) the occurrence of any event, change or other circumstance that could give rise to the termination of the Business Combination Agreement or could otherwise cause the Business Combination to fail to close; (5) the amount of redemption requests made by Leo’s shareholders; (6) the inability to obtain or maintain the listing of the post-business combination company’s common stock on the New York Stock Exchange following the proposed Business Combination; (7) the risk that the proposed Business Combination disrupts current plans and operations as a result of the announcement and consummation of the proposed Business Combination; (8) the ability to recognize the anticipated benefits of the proposed Business Combination, which may be affected by, among other things, competition, the ability of the combined company to grow and manage growth profitably and retain its key employees; (9) costs related to the proposed Business Combination; (10) changes in applicable laws or regulations; (11) the possibility that DMS or the combined company may be adversely affected by other economic, business, and/or competitive factors; and (12) other risks and uncertainties indicated from time to time in the proxy statement relating to the proposed Business Combination, including those under “Risk Factors” in the Registration Statement, and in Leo’s other filings with the SEC. Some of these risks and uncertainties may in the future be amplified by the COVID-19 outbreak and there may be additional risks that we consider immaterial or which are unknown. It is not possible to predict or identify all such risks. Leo cautions that the foregoing list of factors is not exclusive. Leo cautions readers not to place undue reliance upon any forward-looking statements, which speak only as of the date made. Leo does not undertake or accept any obligation or undertaking to release publicly any updates or revisions to any forward-looking statements to reflect any change in its expectations or any change in events, conditions or circumstances on which any such statement is based.

No Offer or Solicitation

This press release is for informational purposes only and is neither an offer to purchase, nor a solicitation of an offer to sell, subscribe for or buy any securities or the solicitation of any vote in any jurisdiction pursuant to the Business Combination or otherwise, nor shall there be any sale, issuance or transfer or securities in any jurisdiction in contravention of applicable law. No offer of securities shall be made except by means of a prospectus meeting the requirements of Section 10 of the Securities Act and otherwise in accordance with applicable law.

Investor Contact

Sherif Guirgis

Leo Holdings Corp.

(310) 800-1005

guirgis@lioncapital.com

Edward Parker

(646) 677-1864

edward.parker@icrinc.com

Media Contact

Jack Murphy

(646) 677-1834

jack.murphy@icrinc.com