The prime minister sought to dodge an embarrassing defeat in the Commons on Wednesday by revealing the money would be given to councils to carry out the work.
Her spokesman said it would take two years.
The Grenfell Tower blaze on 14 June killed 71 people.
Mrs May told MPs at Prime Minister’s Questions: “Councils and housing associations must remove dangerous cladding quickly.
“But paying for these works must not undermine their ability to do important maintenance and repair work.”
Labour called on Wednesday for a £1bn emergency fire safety fund to pay for unsafe cladding removal and replacement, and the retrofitting of sprinklers.
Since the Grenfell Tower fire, emergency services have visited over 1,250 high-rise buildings, Mrs May said.
She also gave an update on the accommodation of the West London block’s former residents.
She said that 210 households were in need of a new home and 201 have since accepted an offer of temporary or permanent accommodation.
Mrs May’s spokesman said she expects landlords “to take responsibility” in privately-owned tower blocks.
The announcement came as Labour prepared to use an opposition day debate in the Commons to press ministers on their detailed demands on building safety.
Shadow housing secretary John Healey said: “More than 11 months on, the time for warm words is long past, and people are rightly asking why so little has changed since the Grenfell Tower fire.
“A series of commitments made by ministers up to and including the Prime Minister have not been honoured.”
Mrs May also faced criticism for not releasing funds for the Grenfell community earlier this year, with rap artist Stormzy asked on-stage at the BRIT awards: “Theresa May, where’s the money for Grenfell?”