Both players submitted their names to the NFL draft advisory board for evaluation but were not expected to leave school early.
Robinson will return for his third season as Michigan's starting quarterback after completing 142 of 258 passes for 2,173 yards, 20 touchdowns and 15 interceptions last season. He also rushed for 1,176 yards and 16 touchdowns.
His return means he could threaten the Big Ten and NCAA all-time quarterback rushing records.
"It's been a dream to play in the NFL and hopefully after next year that becomes a reality," Robinson said in a statement. "But I wouldn't pass up being here with my teammates and coaches for anything.
"It's my second family. I love my teammates. I love Michigan."
Floyd had 48 tackles, eight pass breakups and two interceptions last season.
"Being around all of the great people here, I just couldn't see myself not being here for my senior year," Floyd said in a statement. "Our team still has work to do and places to go and I want to be part of it."