Despite the 22-year-old forward having a year remaining on his deal with the Minstermen, manager Nigel Worthington has allowed the player to leave the club on a free transfer.
Gulls boss Chris Hargreaves, whose team was relegated from the Football League last season, told their official website: 'We have a young, hungry striker, who plays on the shoulder of defenders, is good in the air, quick and scores goals.
"I've always liked him and he's ready to prove a point. He comes straight into pre-season tomorrow and he's really happy to be down here. There were lots of clubs chasing him, including some of our rivals, so I'm delighted to have him.'
Bowman joined York from Hereford in 2013 and he made 43 appearances last season, scoring eight times. He has signed a two-year deal at Plainmoor.
Worthington told the York Press: "We wish Ryan all the best for the future."