The rocker, 50, and his unnamed French girlfriend secretly welcomed the tot into the world almost a year ago, according to the Irish Independent newspaper.
Clayton is the last member of the rock supergroup to become a father.
Details of the birth and the identity of the mother are being kept a closely guarded secret - but insiders tell the publication the baby was a boy.
An source tells the Independent that the bassist is "deliriously happy with fatherhood".
Clayton was previously engaged to supermodel Naomi Campbell and longtime Canadian girlfriend Susie Smith - but both romances fizzled out.
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