The 29-year-old has signed a two-year deal – with Town able to extend their by a further year should they wish.
And boss Steve Cotterill believes it will be 'money well spent'.
"He's all action, he does everything," said Cotterill. "He's played up front by himself which is a rarity these days with strikers.
"He runs hard, he runs quick and he runs in behind teams which is another rarity.
"He holds the ball up well and has a good touch for a big man.
"He scored 14 goals last season, none of them penalties. I don’t see any reason why he won’t score as many goals here as he has for Exeter.
"There is a shortage of free agents up top at the moment. We’ve ended up paying a fee for Ryan but I think it will be money well spent."
Bowman has represented clubs both sides of the Scottish border, beginning his career at Carlisle United and going on to play for Hereford United, York City, Torquay United and Gateshead.
While with non-league Hereford, Bowman helped shock Shrewsbury in the first round of the FA Cup, scoring twice in a 3-1 triumph for the Bulls in November 2012.
After impressing for Gateshead, he earned his move to Motherwell in the Scottish Premiership before moving south to sign for Exeter in January 2019.
Since then, he has scored 34 goals in 112 appearances for the Grecians.