The child, who the couple have named Kai Wayne Rooney, was born at 2.20pm at Liverpool Women's Hospital, their spokesman said.
The spokesman added: "Mother and baby are both absolutely fine. Wayne and Coleen are thrilled with the wonderful addition to their family life."
Earlier, Rooney, 24, missed a training session for his club Manchester United amid growing speculation that his wife was set to give birth.
He will almost certainly be excused from playing for his side in their next fixture against CSKA Moscow at Old Trafford on Tuesday.
News that Coleen, 23, was pregnant emerged earlier this year although rumours had regularly circulated since the couple's spectacular wedding on the Italian Riviera last summer.
Coleen is the eldest of four children to bricklayer dad Tony and nursery nurse mum Colette. Wayne is the eldest of three. Both have large extended families.
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