The on-again-off-again couple is now on again ... Chris Brown

Chris Brown says he's back with Karrueche because she finally realized he did NOT have sex on a St. Tropez yacht.

The on-again-off-again couple is now on again ... and Chris says it's because Karrueche now realizes he was telling her the truth when he said he was not having sex with anyone else.

Sources close to Karrueche tell us ... he was frantically texting and calling her -- more than 20 attempts a day -- to acquit himself, but she ignored him.

We're told Saturday ... Karrueche showed up at Chris' celebrity flag football game to talk it out ... which they did, and she believes him.

As for the whole yacht thing ... there definitely was smoke ... he was on the vessel cavorting with several women, including one of Karrueche's close friends.

Chris did cop to something ... he promised Karrueche he would slow down the partying and treat her better.

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