The couple, who has been married for four years, announced the news of their baby's birth in a personal ad in the Irish Times, reported The Independent.
"Adam and Mariana Clayton are delighted to announce the birth of their beautiful baby girl Alba," they wrote.
No further details about the baby have yet been provided.
Clayton, 57, tied the knot with Mariana in Dublin in 2013.
The bass guitarist of the rock band U2 was engaged to supermodel Naomi Campbell for a brief time in 1994. Their relationship ended the same year.
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