Clement, dismissed by Scottish Premiership club Rangers in February, faces a tough task, with the former Premier League team second from bottom of the English second tier.
Manning, appointed in June, lasted just 17 games - the Canaries lost all of their home league and cup matches under his leadership.
"I'm really excited by this story and opportunity," said former Belgium international Clement, 51, who has signed a contract until 2029.
"I've known of this club for a long time and, whilst we are not in a good moment at this time, we are excited to work together with the players and staff to turn things around."
Norwich, who have taken just nine points from 15 games in the Championship, travel to face Birmingham on Saturday.