Exhibit 15.1

Consent of Independent Registered Public Accounting Firm

To the Supervisory Board

ASML Holding N.V. :

We consent to the incorporation by reference in the registration statements (Nos. 333-116337, 333-126340, 333-136362, 333-141125, 333-142254, 333-144356, 333-147128, 333-153277, 333-162439, 333-170034, 333-188938, 333-190023, 333-192951, 333-203390, 333-219442, and 333-227464) on Form S-8 of ASML Holding N.V. of our report dated February 5, 2019, with respect to the consolidated balance sheets of ASML Holding N.V. and subsidiaries as of December 31, 2018 and 2017, and the related consolidated statements of operations, comprehensive income, shareholders’ equity, and cash flows for each of the years in the three-year period ended December 31, 2018, and the related notes (collectively, the “consolidated financial statements”), and the effectiveness of internal control over financial reporting as of December 31, 2018, which report appears in the December 31, 2018 annual report on Form 20-F of ASML Holding N.V.

Our report refers to a change in accounting for its revenue in 2017 and 2016 due to the adoption of ASC Topic 606 “Revenue from contracts with customers”.

/s/ KPMG Accountants N.V.

Rotterdam, the Netherlands

February 6, 2019