The Vikings announced the moves on Tuesday.
Henderson was one of the Vikings' most consistent players on defense last season, finishing fourth on the team with 91 tackles. He also had eight tackles for loss in his first season as a full-time starter.
Bowman led the Bears with six interceptions and 10 passes defensed in 2009. But he lost his starting job in 2010 and never regained it the past two seasons.
In Minnesota, he'll be relied upon to add depth to a Vikings secondary that struggled last season. The 27-year-old likely will also be used on special teams.