The prime minister agreed to a BBC proposal with the debate set to air on December 9 at 8 p.m. (local time, 20:00 GMT) while Corbyn said earlier in the day he preferred the ITV offer, according to Sky News.
Earlier this week, May told the Sun newspaper that she wanted to explain why her deal was the right one for the United Kingdom and was prepared to discuss it with the opposition leader.
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The debate is therefore expected to be broadcast shortly before the vote on the deal in the House of Commons, scheduled for December 11.
The agreement backed by the UK Cabinet and endorsed by Brussels has faced strong criticism in the UK parliament, with the Irish border solution as one of the key issues.