The 38-year-old star and his wife Kate Norley have welcomed a "happy and healthy" baby boy, reported Aceshowbiz.
"John and his wife Kate are parents of a baby boy. Everybody is happy and healthy," said a representative for HBO that airs "Last Week Tonight".
Oliver and his wife, who served as a US Army medic in Iraq, exchanged wedding vows in 2011.
They first met in 2008 when he was covering the Republican National Convention and she was there on behalf of Vets for Freedom.