Eubank Jr claimed a thrilling points victory over his rival in April in a bout that brought back memories of the epic battles between their fathers Chris Eubank and Nigel Benn during the 1990s and the pair will do it all over again in London this autumn.
The venue for the fight is yet to be announced but is likely to be either the Tottenham Hotspur Stadium or Wembley Stadium.
The rematch will again take place at the middleweight limit of 160 pounds with a 10-pound rehydration clause.
Benn tweeted in response to the news: "Ready to fight now! September 20th can't come soon enough."
Benn's promoter Eddie Hearn is confident that a second fight between the pair "will be even better" than the original as neither man will relent from their attacking style of fighting.
The Matchroom chief told The Ring: "I just think the second fight will be even better. They're not going to change. They're going to come out from the first bell and just carry on like the 13th round. And when you see a fight like that, for me, the automatic thing to do is to do the rematch.
"The fight was always going to be two fights, but sometimes a fight's one-sided or it ends early and there isn't really the appetite for the rematch.
"I think here, now with Conor having that activity, which is something that was lacking from the first fight as well, we really fancy our chances.
"We know the weight's a disadvantage and that showed a little bit in the first fight, but fans can just expect a continuation of the 12th round and it'll be another toe-to-toe war."