The 24-year-old left-back, who made 113 appearances after coming through the ranks at City, will officially move to Adams Park on 1 July.
"We have been on the look-out for a left-back for some time," Wycombe boss Paul Lambert told his club's website.
"He's a natural left-footer who'll give the team balance, and the bonus is he can also play further forward."
Woodman was also loaned out to Torquay (two spells) and Mansfield during his time at Ashton Gate.
BBC