Sources close to the newly engaged couple say Pete and his ex-gf, Cazzie David, were "on a break" in early May -- but not necessarily broken up for good -- when his relationship with Ariana sparked. But they hit if off, and it quickly became clear Pete was serious about moving on with Ariana.

The good news -- it seems all parties involved are happy with the end result. As we reported, Cazzie's not upset or dwelling on her ex's quick rebound. Hey, if it's good enough for Ross and Rachel.

As for Ariana and Pete -- they're still in full PDA mode with Davidson posting a pic wrapped up with his fiancee, captioned ... "u know what you’d dream it be like ? it’s better than that."