"It's been beautiful," he told people.com of his first few weeks as a father.
"Every second you pray that you can keep the kid alive. Every day is different, the time has become very elusive, stuff just goes by so fast. It's just beautiful. I've cried most days; I just stare at him."
The star says that aside from his sleep schedule, his style has changed as well.
Another upcoming milestone for Stamos? His first Father's Day on June 19.
"I know I'll be crying a lot," he says of his plans for the holiday.
"I've been writing Billy a letter that I'm putting away for him to read when he's 18. I'll probably continue writing that, and I'll certainly try to honor my father."
As for Billy, Stamos hopes to do what he can to help make the world a better place by the time his son grows up.
"We live in an anxiety-riddled, unsure, divisive time right now. I think most of us are searching, even subconsciously, to find what's missing from our lives: grace, charity, kindness, and peace, and family, and community and friendship."
"I just hope this world is a better place for Billy when he starts to understand what it's all about. And I just want to be an example to him. I have a real responsibility now. I've never really had real responsibility."
"I thought it was beyond me to have a kid and a great wife, but it's given me a reason to live. Life is in session now."
(With inputs from Vishal Verma)