The resignation came after a story was published in the Charleston Gazette Friday that said Stewart had asked at least two newspaper reporters to "dig up dirt" on assistant coach Dana Holgorsen.
Stewart had already said he planned to leave the school at the end of the 2012 season and Holgorsen was scheduled to replace him. Instead, Holgorsen will take over the job a year earlier than planned.
"Coach Stewart and I have talked these past few days and both believe this is the right thing to do for our football program, our team, our university, our state," Luck said.
Holgorsen was hired Dec. 15 to be both the offensive coordinator and quarterbacks coach during the next season. Stewart had been coach of the Mountaineers since Rich Rodriguez left for Michigan four years ago.
The Gazette reported Stewart had asked the reporters to find anything they could that would be incriminating to Holgorsen. One of the reporters disclosed the conversation this week on a radio program.
"He (Stewart) respects the Mountaineer program and the student-athletes he coaches too much to let any conflict and any perception of disorder continue to be a distraction to the staff, team and fans," Luck said in his statement.
Stewart's teams went 27-12 in his three seasons as head coach. He became an assistant coach at West Virginia in 2000.