Republic of Ireland U21 international Cullen has joined the Addicks for the rest of the season to become the club's fifth signing of the summer.
Bowyer is delighted to sign the central midfielder, who made 12 appearances for Bolton in the Sky Bet Championship in addition to three starts for the Hammers in the FA Cup last season.
He told the club's official website: “He's a very good player, good experience in this league and went to the Championship last season so we thought he was going to be out of our reach.
“I think he's a great addition to the squad. He's a very good player in and out of possession so he'll be a good addition for us. I've always said I only want players that improve us, and he improves us."