"This is an exciting time for Rutgers," Rutgers coach Greg Schiano said in a statement. "I'm so happy for our players to be able to experience a great bowl game atmosphere. Anytime you can go out and test yourself against the country's top talent, it creates a tremendous opportunity for our players to grow and develop."
The Gator Bowl is still scheduled to be played Dec. 31 in Jacksonville, Florida (11 a.m. ET, ESPN).
"Our outstanding group of seniors deserves this proper send off as we compete for a championship next week," Wake Forest coach Dave Clawson said in a statement. "[Rutgers] coach Greg Schiano does a great job and I have tremendous respect for him and his staff. We expect a very tough game against a talented and well-coached team."
Earlier Thursday, the NCAA Division I Football Oversight Committee decided that the previous guidelines for selecting 5-7 teams to fill bowl openings would remain, with the highest multiyear Academic Progress Rate being the greatest determining factor.
That meant Rutgers had the first opportunity among the 5-7 teams eligible to be the replacement.
Texas A&M withdrew from the game Wednesday because of COVID-19 cases and other issues that affected its roster of available players. Texas A&M athletic director Ross Bjork told ESPN that the program was down to 38 scholarship position players, of which 20 were offensive and defensive linemen.
The NCAA football oversight committee also announced on Thursday that any bowl game can be moved to as late as Jan. 10 if the schools involved need additional time to prepare.
The Scarlet Knights last played Nov. 27 against Maryland and were eliminated from bowl consideration a week later when eligible teams filled every spot.
Rutgers last appeared in a bowl game in 2014, the second-longest postseason drought among Power 5 teams, behind Kansas. It will be the Scarlet Knights' seventh bowl appearance with Schiano as coach.
Illinois (5-7) on Wednesday had communicated its desire to replace Texas A&M, sources told ESPN.
ESPN's Andrea Adelson, Adam Rittenberg, Mark Schlabach and The Associated Press contributed to this report.