Sources close to the couple tell TMZ ... Caitlin is now living under the same roof as the "Magic Mike" hunk, and so far, they're relishing every moment of cohabitating.

We're told they're very much in love, especially after forging quite a strong bond over their Pittsburgh roots -- even traveling there together, and further solidifying their relationship with trips to NYC and Italy.

Most importantly, our sources say the actor's beloved pet dog Bubbles has given Caitlin his seal of approval ... which means a lot to Joe.

News of Joe's romance with COC emerged in September last year ... just 2 months after he filed for divorce from Sofia after 7 years of marriage. The main reason they called it quits was his desire to have kids and Sofia's reluctance to have them.

TMZ broke the story last week their divorce was settled amicably -- each kept the assets they accumulated individually, and both mutually waived any right to spousal support.

While Joe quickly found new love after their split, Sofia moved on too ... now dating a respected orthopedic surgeon named Justin Saliman -- they've been seen out on several date nights over the past few months.

But back to Caitlin ... Joe hit it off with the rising actress after meeting at a 'Winning Time" after-party -- she played Dyan Cannon in that series -- and later going public as a couple at NYC's Children of Armenia Fund Gala in December.