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 (No. 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 11, 2020, with respect to the consolidated balance sheets of ASML Holding N.V. and subsidiaries as of December 31, 2019 and 2018 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, 2019, and the related notes, and the effectiveness of internal control over financial reporting as of December 31, 2019, which report appears in the December 31, 2019 annual report on Form 20-F of ASML Holding N.V.

/s/ KPMG Accountants N.V.

Rotterdam, the Netherlands

February 12, 2020