Caldwell was signed as a UDFA by the Colts out of William and Mary (where he was a teammate of Giants' DE Adrian Tracy). He started 13 games for Indianapolis in 2011, but was waived in camp this year and did not catch on with another club this season.
Bryant, an Ohio State product, broke in as a UDFA with the Rams in 2011 and has spent time on the practice squads of the Panthers and Browns.
DeGeare was a fifth-round selection of the Vikings in 2010 out of Wake Forest. After being released by the Vikings during the final cuts last September, DeGeare was signed to the Titans' practice squad.
The signings bring the total of futures deals to 13 so far this month for the Giants.
Previously signed: QB Curtis Painter, DT Bobby Skinner, DB Trumaine McBride, LB Jake Muasau, OL Michael Jasper, WR Kevin Hardy, WR Brandon Collins, T Levy Adcock, DE Matt Broha, TE Larry Donnell, OL Stephen Goodin, T Matt McCants and DB Laron Scott