, have welcomed their first child, a boy, her manager confirmed to People magazine Tuesday.Jett Hamilton Roberts
was born at 4:20 p.m. on Monday. He weighed 7 lbs., 8 oz.
Scott, who stars on HBO's new series "The No. 1 Ladies' Detective Agency," based on the popular novels byAlexander McCall Smith
, discovered she was pregnant shortly before leaving for Botswana to film the show.
"At one point I was trying to gain weight for the role, and I noticed I had put on 7 lbs. in 7 days. And I thought, my god! What's going on here," she tells "People."
"I thought something was wrong with me, and I found out I was pregnant the day I was supposed to leave for Africa."
She first revealed her pregnancy to reporters at the Television Critics Association conference in Los Angeles in January.
"The first trimester I spent in Botswana," said Scott, 37, a three-time Grammy Award winner. "That was one of the biggest challenges of my life. First trimester! You're sick every morning. It was seven hours time difference, the heat, the bugs, the 14 hour days."
But Scott continued filming through her pregnancy: "My doctors gave me a clean bill of health and said you can do this, so I did it."
The new parents, who reportedly began dating in 2007, announced their engagement at a concert in New York City on June 20.
"I definitely had issues over the course of my life, reproduction issues," she explains to PEOPLE. "I was married for five years and could never conceive a child. Until now ... It's the most amazing thing that's ever happened to me."