Governor Deval Patrick announced Friday that he is replacing his state secretary of labor and workforce development, Joanne F. Goldstein, who had been facing questions about the troubled launch of the state’s new online unemployment benefits system built by Deloitte Consulting.

In a press release, Patrick said Goldstein will be replaced by Rachel Kaprielian, who is currently the state’s registrar of motor vehicles. As registrar, Kaprielian entered a $76.8 million contract with Deloitte in 2012 to overhaul that agency’s online system.

No replacement at the registry has been announced.

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Goldstein will be taking a job as an associate vice president at Northeastern University.

Patrick at a State House press conference Friday thanked Goldstein for her service and downplayed problems that have plagued the unemployment website as a reason for her departure.

Asked whether the new secretary could hold Deloitte’s feet to the fire, Patrick insisted she could.

Goldstein, in a brief interview after the press conference, said she feels she is leaving the unemployment system in good shape. As to the timing of her departure, she said it was simply a job offer too good to resist.

Goldstein has faced criticism after state officials negotiated a flawed $46 million contract that provided few protections for taxpayers and little oversight of consultants.

When the Deloitte project rolled out in July, it was two years late and $6 million over budget; it was riddled with technical problems and left hundreds if not thousands of users struggling to get unemployment benefits, the Globe has reported.

Because of the Globe’s report and an onslaught of phone calls from angry claimants, the legislature’s Senate Post-Audit and Oversight Committee began an investigation to examine problems with the computer system last fall. The committee, chaired by State Senator Cynthia Stone Creem, a Newton Democrat, is expected to conduct another hearing, likely this month.

Patrick did not mention those issues in his press release, or offer any reason for the abrupt change in his Cabinet.

“I sincerely thank Joanne for her four years of dedication and commitment to our workers, job seekers and employers through some of the Commonwealth’s most challenging economic times,” Patrick said in a statement. “I am thrilled that Rachel has agreed to take on this new role, and I am confident that she is prepared to continue the difficult work of getting our residents back to work, and preparing both our workers and employers for the jobs of the 21st century economy.”