Exhibit 99.1

CONSENT OF JEFFERIES LLC

May 18, 2018

The Conflicts Committee of the Board of Directors of

Rice Midstream Management LLC

625 Liberty Avenue, Suite 1700

Pittsburgh, PA 15222

We hereby consent to the inclusion of our opinion letter, dated April 25, 2018, to the Conflicts Committee of the Board of Directors of Rice Midstream Management LLC as Annex B to the proxy statement/prospectus which forms a part of the Registration Statement on Form S-4 of EQT Midstream Partners, LP relating to the proposed transactions in the merger agreement (as defined therein), and to the references to such opinion and our firm in such proxy statement/prospectus under the captions entitled “Summary—Opinions of the Financial Advisor to the RMP Conflicts Committee”, “Risk Factors—Risk Factors Relating to the Merger”, “The Merger—Background of the Merger”, “The Merger—Recommendation of the RMP Board and the RMP Conflicts Committee; Reasons for the Merger”, “The Merger—Opinion of the Financial Advisor to the RMP Conflicts Committee”, and “The Merger—Unaudited Forecasted Financial Information.” By giving such consent, we do not admit that we come within the category of persons whose consent is required under the Securities Act of 1933, as amended (the “Securities Act”), or the rules and regulations of the Securities and Exchange Commission thereunder, nor do we hereby admit that we are experts with respect to any part of such Registration Statement within the meaning of the term “expert” as used in the Securities Act, or the rules and regulations of the Securities and Exchange Commission thereunder. Notwithstanding the foregoing, it is understood that our consent is being delivered solely in connection with the filing of the above referenced Registration Statement and that our opinion is not to be used, circulated, quoted or otherwise referred to for any other purpose, nor is it to be filed with, included in or referred to in whole or in part in any registration statement (including any subsequent amendments to the above referenced Registration Statement), proxy statement or any other document, except in accordance with our prior written consent.

Very truly yours,

/s/ JEFFERIES LLC

JEFFERIES LLC