The couple announced their baby girl's arrival with a personal advert in Tuesday's Irish Times.
"Adam and Mariana Clayton are delighted to announce the birth of their beautiful baby girl Alba," read the announcement.
Adam and Mariana wed in 2013, celebrating on the French Riviera at the 14th-century château in Mandelieu-la-Napoule near Cannes, according to the Irish Times. The musician is already a father to a son born in 2010 from a previous relationship.
Last month, Clayton was honored with the Stevie Ray Vaughan Award at the MusiCares MAP Fund concert in New York City for his work with the charity, which helps musicians with addiction recovery. During his speech he thanked his bandmates, who supported him through his battle with alcohol.
"I was lucky because I had three friends who could see what was going on and who loved me enough to take up the slack of my failing," Clayton expressed. "Bono, the Edge, and Larry [Mullen] truly supported me before and after I entered recovery, and I am unreservedly grateful for their friendship, understanding and support."
U2 is currently on their Joshua Tree Tour, finishing off their European leg before they head Stateside. For more on the rock band, watch below.