The move was announced before the start of practice at training camp in suburban Rochester on Tuesday. Stahovich was signed by Buffalo in April to compete with Powell.
He was cut two days after the Bills' preseason-opening 44-20 win at Indianapolis. Stahovich averaged 41.3 yards on three punts, landing two of them inside the 20.
Stahovich played at San Diego State, and was initially signed with Indianapolis last year. He was cut before the start of the season.
Powell replaced long-time veteran Brian Moorman in taking over the punting duties in Buffalo a month into last season.