The baby, a boy named Henry Günther Ademola Dashtu Samuel, was born late Monday in a Los Angeles-area hospital. Everyone is "happy and healthy," a source tells PEOPLE.
The couple will soon bring the baby – who carries the last name of his dad, born Sealhenry Samuel, and got the name Günther from Heidi's father – home to their Bel Air estate to join Klum's 16-month-old daughter, Leni.
This past March, Klum and Seal announced they were expecting a child together. On May 10, they were wed on a beach in Mexico, near Seal's home on Mexico's luxurious Costa Careyes.
Klum, 32, had Leni with her ex-boyfriend, Italian businessman Flavio Briatore. But from the start of Seal's and Klum's romance, which began while Klum was pregnant with Leni in February 2004, the singer, 42, has acted like a father to the little girl.
As a pal told PEOPLE, "He is crazy about Leni. He is always carrying her around. He is the first one to change a diaper."
"What I love most about fatherhood," said Seal, is "the opportunity to be a part of the development process of a new life."
As for Klum, earlier this year she said during an interview on German TV about her life with Seal and Leni, "We all sing a lot together. I sing a lot, even with my voice."
And now they have a quartet.