The Liberty X singer gave birth to a baby boy yesterday.
Kevin flew back from the World Twenty20 cricket tournament in the Caribbean to be by his wife's side.
'Both baby and Jessica are doing brilliantly,' their spokeswoman tells the Daily Mirror.
'Kevin made a dramatic last-minute flight from Barbados to arrive for the birth.
'He will stay with Jessica for a couple of days before returning to the West Indies to continue the tournament.
'They would now like to spend time on their own to enjoy and relish every minute of their new arrival.'
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