The broadcaster also said it hopes “to hear soon from the Labour Party” on whether leader Jeremy Corbyn will join the TV event, which will air on Sunday December 9.
The BBC has not yet confirmed a channel or time for the broadcast.
However, there was no mention of a place for any other parties, which Scottish First Minister Nicola Sturgeon slammed as a ‘travesty’.
But in a tweet on its news press feed, it said: “We’ve just heard the Prime Minister has accepted the BBC’s offer to take part in a debate on the Brexit deal on Sunday December 9.
“We’re delighted she’s agreed and hope to hear soon from the Labour Party.
“We have been discussing debate formats with both parties and will announce further details soon.”
In reply, Nicola Sturgeon tweeted: “If this or any Brexit TV debate goes ahead without all options - including that of remaining in the EU - being included and given a voice, it will be an absolute travesty of democracy.”
Downing Street and the Leader of the Opposition’s office are believed to have sat down with the four main broadcasters to hear their pitches before deciding on who to go with.
Number 10’s preference is said to have been with the BBC, as it was the most “rounded” and focused on the Prime Minister’s deal, not the wider political situation.
The BBC had initially suggested the debate would place on Thursday December 6.
But after Mr Corbyn’s office expressed a preference to go with ITV’s offer of a Sunday night broadcast, it offered to switch to Sunday as well.
Downing Street was reportedly happy to go with that option, and it is now waiting for Labour to say whether it is willing to proceed.
Appearing on TV show This Morning, Mr Corbyn said the ITV offer was “the most sensible”.
A spokesman for the Labour leader declined to comment on the BBC’s announcement.
But a Labour source suggested the party prefers ITV’s offer, saying its pitch was stronger and in a better slot.
It is believed ITV has been willing to move the final of I’m A Celebrity... Get Me Out Of Here! to accommodate the head-to head between Mrs May and Mr Corbyn.