Future and Ciara Back Together For Good Of Their Baby

9/3/2014 11:15 AM PDT

Future and Ciara -- Back Together For The Good Of Their Baby

Exclusive Details

Future
and Ciara didn't stay apart for long ... and it's all because Ciara feels strongly about her son needing his father around 24/7.

Sources close to Future tell TMZ ... he and Ciara are living together again -- and trying to make things work between them -- so Future can help take care of their 4-month-old son, Future Zahir.

Ciara must be willing to overlook the past ... since she was the one who claimed Future cheated on her while he was on tour -- and then broke off their engagement last month.

We're told Ciara wasn't interested in a shared parenting situation ... saying she believes Future's a good father and that it's best for their son if his dad's there.

Pretty selfless of her, if she really believes he cheated.