"She's head over heels," a source close to the pop star, 26, tells PEOPLE in its new cover story. "She's telling friends, 'I'm in love.' "
The most important thing to Joe? "If my daughter's happy, then I'm happy," he says. "And if she finds love, then I'm in love with the fact that she finds happiness. It's been a tough year for her. A lot of disappointment. And my greatest joy as a father is to see my baby be happy."
Simpson and Mayer, 28, first met when Simpson was still married to Nick Lachey, 32. After her November 2005 separation, they bumped into each other again in June at the New York City nightclub Double Seven, where a source tells PEOPLE Simpson was "flirting up a storm" with both Mayer and actor Jared Leto.
Eventually Mayer, who's currently touring with Sheryl Crow, passed the ultimate test: He babysat Simpson's maltipoo, Daisy. "If you're in with Daisy," a Simpson pal tells PEOPLE, "you're in with her!"
Reporting by CARRIE BORZILLO-VRENNA, JEFFREY SLONIM and MICHELLE TAN