The decision follows a summer which saw thousands of holidaymakers affected by a backlog in applications, which peaked at 537,663 in late June.
The changes mean the Passport Office's chief executive Paul Pugh will be replaced.
He will remain until a successor - working as director general - is named.
Mrs May had been forced to introduce a number of emergency measures to tackle the backlog, which is now around 80,000.
But earlier this month, the Home Affairs Committee said passport applicants who paid more than Â£30 extra for a "fast-track" service had been "exploited" and should receive a refund.
Announcing the changes, Mrs May said: "As the events of the summer showed, it is essential that HMPO is run as efficiently as possible and is as accountable as possible."
The move to the Home Office will take effect from 1 October.
Speaking to MPs earlier this year, Mr Pugh denied union claims that the closure of 22 passport centres and the loss of 550 jobs - as well as the closure of the overseas units - had caused the crisis.
The PCS union, which represents civil servants, described the news as welcome "if it means the jobs we've called for, equal pay for staff and no more privatisation".
Earlier this month, the Home Affairs Committee said the Passport Office should lose its agency status and be brought under direct ministerial control following an "appalling series of failures".
The Home Office also said it is reviewing the emergency measures introduced at the height of the crisis:
The UK's Passport Office is to be brought under Home Office control and made accountable to ministers, Home Secretary Theresa May has announced.