LOS ANGELES (Nov. 21) — After keeping the entertainment world on its toes for weeks, Ashlee Simpson and Pete Wentz have become first-time parents, PEOPLE is reporting.

The musical duo had a baby boy on Thursday, naming their new child Bronx Mowgli Wentz. A rep for the couple tells PEOPLE: “Ashlee, Pete and baby Bronx are all healthy and happy, and thank everyone for their well wishes!”

Simpson and Wentz married amid a swirl of pregnancy rumors in May. They had announced their engagement just a month earlier, fanning the flames of the baby rumor mill as bloggers and tabloids presumed the quick nuptials were a sure-fire sign of a pregnancy.

While the couple never gave a due date, many suspected Ashlee would give birth in early October. As of Oct. 30, Wentz told PEOPLE he was “on call permanently” for when Ashlee went into labor. Even then, he said she was “at the very end, and it could happen at any point.”

He said Simpson was doing well with the pregnancy, but that it was getting a bit old by now.

“I think she wants to just be not pregnant anymore … It’s a struggle to go up and down the stairs. Going out in public is insane,” Wentz said. He also said that he and Ashlee didn’t plan on naming the baby until after it was born. “I want to meet [the baby] first,” he said, joking that a friend told him: “You’ve gotta have a baby with a name that could be a rock star or a senator, so he’ll get work either way.”

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Speaking with PEOPLE on Nov. 7, ‘Papa’-soon-to-be-Grandpapa Joe Simpson said of Ashlee: “The day she found out she was pregnant, she became a woman.” He went on to say that his daughter is “concerned about what she eats and how she prepares for the child and [details like], is the baby’s room ‘green’ enough? It’s a transformation you never expect as a parent — you pray for it, but never expect it. She’s ready for this baby!”