Demps currently is in route to Orlando, Fla., to sign his deal.
Patriots coach Bill Belichick commented Thursday that the team was in need of a kick returner, a role that Demps filled at the University of Florida. Demps also is expected to play in the backfield and possibly at slot receiver.
Demps rushed for 2,470 career yards and 23 touchdowns while at Florida, but he went undrafted in April while choosing to focus on his Olympic career. Demps didn't attend any college football all-star games or participate in NFL predraft workouts.
Demps won a silver medal as a member of the 4x100-meter relay team in London.
UPDATE: Demps has officially signed with the Patriots, the team announced Friday night. Financial terms were unavailable, but a source with knowledge of the situation told NFL.com and NFL Network reporter Ian Rapoport that Demps' contract is for three years.
To everyone wondering, yes it's true I'mnow a new England patriot. Glad to be apart of the team. It's truly an honor.â Jeffery Demps (@jeffdemps7) August 18, 2012
Follow Ian Rapoport on Twitter @RapSheet