The 39-year-old actor, who previously dated actresses Zoe Saldana and Renee Zellweger, got divorced from Jennifer Esposito in 2007, reported Contactmusic.
"She's wonderful, the one for me. It feels great," Cooper said.
The actor's mother Gloria is reportedly backing the couple, who were recently spotted cosying up to one another at an award show.
"Gloria's been really won over by Suki. She's backing Bradley all the way if he wants to tie the knot with her," a source said.