Inside Bradley Cooper's Life as a Dad: 'He's a Changed Person'

All about Bradley Cooper's life at home with girlfriend Irina Shayk and daughter Lea

Although Bradley Cooper is riding a professional high — his directorial debut, A Star is Born, has earned eight Oscar nominations and more than $400 million at the worldwide box office — the 44-year-old actor’s home life is where his heart is, ever since his daughter Lea, 22 months, was born.

“Bradley is like a changed person,” a source tells PEOPLE in the new issue about how Cooper has embraced parenthood with girlfriend Irina Shayk, 33. “Becoming a dad seems to be such a positive experience for him.”

Bradley Cooper and Irina Shayk. Jamie McCarthy/Getty Images for National Board of Review

Lea De Seine Shayk Cooper was born on March 21, 2017 in Los Angeles. She is the first child for Cooper and the Russian supermodel, who have been dating since 2015.

Although Cooper and Shayk are fiercely private, “they are very active with [Lea],” says the source. “They go for neighborhood walks, visit the farmer’s market, play on the beach, or take Lea to a toddler class.”

Bradley Cooper. Daniele Venturelli/WireImage

Recently Cooper and Shayk have made a few rare public appearances together to support A Star Is Born. They attended the Golden Globes on Jan. 6 — where Shayk lovingly straightened his bow tie at their table — and she joined him at the National Board of Review Awards Gala in New York on Jan. 8.

And despite the fact that Shayk has often worn a large emerald ring on that finger for more than two years, the source says that right now co-parenting is more important to the couple than getting married: “They’re focused on their daughter, and they seem happy together.”

For much more on Cooper and Shayk, pick up the latest issue of PEOPLE, on newsstands Friday.