The defensive tackle from Syracuse was selected in the third round, seventh overall, in last month's draft. He had 121 tackles, 25 1-2 for losses, and 13 sacks with the Orange.
Bromley was the last of the team's seven draft picks to sign a contract.
New York also signed free agent linebacker Terrell Manning, who has played in six regular-season games, five with Green Bay in 2012, one with San Diego last season. He also was with the Packers for two playoffs games in 2012.
Manning was a fifth-round pick by the Packers in 2012.
The Giants open their mandatory minicamp Tuesday.