Future and Ciara are done for good … the engagement is off and they are officially single … sources connected with the former couple tell TMZ.

Ciara is the one who did the breaking up … she claims he was cheating on her while on tour.

It’s complicated … because they have a 3-month-old son, Future Zahir. We’re told she has the kid and fully intends to get custody.

As for Future’s response to Ciara’s allegations … so far he’s radio silent.

Source TMZ: Future and Ciara broken up. She takes the kid.