Arnett transferred to Michigan State from Tennessee following his freshman year to be closer to his ailing father, William, who is waiting for a kidney transplant and is on dialysis.
Arnett, a native of Saginaw, Mich., enrolled at Michigan State in January and practiced with the team this spring.
Coach Mark Dantonio called him with the news late Thursday morning.
"I didn't even know it was coming today," Arnett told ESPN.com. "It was a big surprise. It was a big relief off my back. I was able to really take a deep breath and just focus on being a student-athlete."
Arnett said his dad "was just happy" when he learned his son will be able to play for the Spartans right away.
"He's really looking forward to it," Arnett said. "He's excited, man. When I talked to him, that's all he talked about, being able to see me play."
The waiver means Arnett does not have to sit out a season, as NCAA transfer rules require. He has three years of eligibility remaining.
Arnett had 24 receptions for 242 yards and two touchdowns as a freshman for the Volunteers last season.