Exhibit 31.1

CERTIFICATION PURSUANT TO

RULE 13a—14(a) or RULE 15d—14(a)

OF THE SECURITIES EXCHANGE ACT OF 1934

I, William J. Miller, Ph.D., certify that:

1. I have reviewed this annual report on Form 10-K/A for the year ended December 31, 2018 (the “Report”) of the Company; and

2. Based on my knowledge, this report does not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements made, in light of the circumstances under which such statements were made, not misleading with respect to the period covered by this report.

/s/ WILLIAM J. MILLER, Ph.D.

William J. Miller, Ph.D.

Chief Executive Officer and Director

Veeco Instruments Inc.

May 1, 2019