Ross, the Giants' vice president of player evaluation, had been a top lieutenant of previous general manager Jerry Reese and oversaw the team's drafts. He was one of four candidates to interview for the general manager job.
"I worked with Marc when I was with the organization before," Gettleman said in a statement released by the team. "I have great respect for him and high regard for his work. Clearly, we're going in a different direction, but that doesn't make these kinds of decisions any easier."
Ross joined the Giants in May 2007 and was completing his 11th season with the team, including his fifth as VP of player evaluation. He had spent the previous six years as New York's director of college scouting.
Hart, who started seven games at right tackle this season, reportedly told coaches that he would not play in Sunday's season finale against the Washington Redskins. A source told ESPN's Jordan Raanan that starting left tackle Ereck Flowers also told coaches he would not play against Washington.
Both Hart and Flowers have checked out and are ready for the Giants' season to end, the source said.
Hart, a seventh-round pick out of Florida State in 2015, told NJ Advance Media before the season started that he was "the best right tackle in the league." His waiving was first reported by NorthJersey.com.
In other roster moves Saturday, the Giants placed wide receiver Tavarres King on injured reserve and promoted offensive linemen Adam Bisnowaty and Nick Becton and tight end Ryan O'Malley to the active roster from the practice squad.
King suffered a concussion in Week 15 against the Philadelphia Eagles and is the 23rd Giants player on injured reserve, according to the team.