"Jonathan is a very good football player who has accomplished many great things during his first four years in the CFL," Stampeders general manager and coach John Hufnagel said in a statement. "I look forward to seeing him do the same as a member of the Stampeders."
Hefney had 74 tackles last year, four fumble recoveries, one sack, one forced fumble and one interception.
But he ran afoul of the Bombers after being arrested for marijuana possession in his native South Carolina on May 31. Hefney did not notify the team promptly about the incident.
After playing in last week's first exhibition game against Toronto, the Bombers released the 28-year-old.
Hefney joined Winnipeg in 2009 and was named CFL East rookie of the year that season.
He has been named a league-wide all-star on two occasions.