Chris Brown says he has officially BROKEN UP with his  girlfriend Karrueche Tran ...  explaining, "I don't want  to see her hurt over my friendship with Rihanna."

Brown  just made the announcement ... saying, "I have decided to be single to focus on  my career. I love Karrueche very much but I don't want to see her hurt over my  friendship with Rihanna."

He adds, "I'd rather be single allowing us to  both be happy in our lives."

The announcement comes after Brown and  Rihanna were spotted together at the Jay Z concert in Brooklyn last night. The  two had been hanging around each other A LOT lately ... and did some hardcore  flirting at the MTV VMAs.

Karrueche had posted a cryptic tweet last  night reading, "Bye baby."

Now it makes sense.