The boy, named Zachary Jackson Levon Furnish-John, is the first for the British rock star and Canadian filmmaker David Furnish, who have been together since the early 1990s.
"We are overwhelmed with happiness and joy at this very special moment," US Weekly quoted the pair as saying. "Zachary is healthy and doing really well, and we are very proud and happy parents."
The magazine said the boy weighed 7 pounds, 15 ounces, and it quoted a representative for the 63-year-old musician as saying that no further details about the surrogacy arrangement would be disclosed. John's spokeswoman told Reuters the report was accurate.
The pair, who entered into a civil union in 2005, tried to adopt an AIDS-infected orphan in Ukraine last year, but were thwarted by government regulations.
Their son's middle name is a possible nod to John's 1971 song "Levon," whose lyrics were written by the rocker's longtime collaborator Bernie Taupin and inspired by Levon Helm, the drummer and singer for The Band.