The longtime bachelor bassist, 53, wed Brazilian model Mariana Teixeira de Carvalho in a simple ceremony in Dublin on Wednesday, he was "delighted to confirm" to PEOPLE via his rep.
The couple have been dating for four years and became engaged earlier this year when Clayton popped the question in Mariana's native Brazil during Carnival, according to BBC News.
Bandmate The Edge was seen snapping photos of the happy couple on the streets of Dublin the day they exchanged vows.
The bride was all smiles in a white knee-length dress and sheer jacket, while Clayton looked equally jolly – and dapper – in a blue suit and purple tie.
This was Clayton's first trip down the aisle, although he was engaged twice before – once to supermodel Naomi Campbell in 1994 and again to Suzie Smith, reportedly a former assistant to band manger Paul McGuinness, in 2006.
Per the BBC, the newlyweds are expected to have a three-day wedding celebration in France with 150 guests beginning Friday.