Adam was a restricted free agent after being tendered a contract offer by the team last month.
He was selected in the second round of the 2008 draft, and has played parts of four seasons with the Sabres. Adam has 15 goals and 11 assists for 26 points in 87 NHL games.
Last season, he led Buffalo's AHL affiliate in Rochester with 29 goals and finished second on the team with 49 points.
Adams was the AHL's rookie of the year in 2010-11.