The Kings of Leon guitarist and wife Johanna Bennett welcomed a son into the world in Nashville, Tennessee, on April 22 and the 6lb 10oz boy has been named Knox Cameron Patrick.
A spokesperson for the couple said: "Mother, father and baby are happy and healthy and doing well."
News of Johanna`s pregnancy only emerged in March, with insiders at the time revealing the couple and the musician`s bandmates, his cousins Caleb, Jared and Nathan Followill, were "thrilled" by the news.
A source said at the time: "They are both absolutely thrilled and can`t wait to become a proper family.
"The rest of the band are just as happy as they are and are looking forward to meeting the new arrival as he or she will be the first Kings of Leon baby."
The baby`s arrival has come just weeks before the American rockers return to the British stage, when they play Ireland`s Slane Castle in May and the Isle of Wight festival a few weeks later.
Matthew and British-born Johanna - who has previously dated Arctic Monkeys frontman Alex Turner - married in November 2009, two years after they first started dating.