Tressel, Ohio State's head coach since 2001, took the Buckeyes to a national championship in 2002 and has an overall coaching record of 106-22.
"After meeting with university officials, we agreed that it is in the best interest of Ohio State that I resign as head football coach," Tressel said in a statement released by the school Monday. "The appreciation that (wife) Ellen and I have for the Buckeye Nation is immeasurable."
In December, OSU announced that five players, including quarterback Terrelle Pryor, would be suspended for the first five games of the 2011 season for receiving improper benefits in 2009.
In January, school officials learned a former Buckeye had informed Tressel of the potential violations the previous April.
Tressel did not alert the school to the possible rule infringements and also signed an NCAA compliance form that indicated he knew of no potential violations in the football program.
Assistant coach Luke Fickell will serve as interim coach for the 2011 season, the school said.