ANN ARBOR, Mich. -- Brady Hoke had enough time at Michigan, but not enough wins, interim athletic director Jim Hackett said Tuesday night.

Hackett formally announced his decision to fire the Wolverines' head coach shortly after Hoke shared the news with his team Tuesday afternoon. Hoke ends his four-year tenure in Ann Arbor with a 31-20 record. Hackett said the universal respect players and peers held for Hoke made his choice a difficult one.

"This was not an easy decision," Hackett said. "Everywhere I go there is zero question about Brady's values."

Hoke did not leave through the front doors of Schembechler Hall, the team's practice facility, but released a statement about his departure.

It said, in part: "I want to thank all of the sons that played for our teams and appreciate the commitment that our coaches and support staff made to the program every day. I will miss the relationships that I've been fortunate enough to make within this university and community."

Players left the team's practice facility teary-eyed after meeting with Hoke. Hackett said he spoke briefly with the team this afternoon, but didn't want to interfere with Hoke's final meeting with his players. He said he intends to talk more with the players about what criteria they feel are important in a new coach at a later date.

The search for Hoke's replacement will begin immediately, according to Hackett. He defined the criteria for candidates as "winning with the shared values of the University of Michigan."

Hackett said he has a specific deadline in mind for when he wants to have a new coach in place, but did not share that date publicly. He plans to use an executive search firm that is familiar with Michigan and its athletic department to help make the process run smoothly.

He was explicit in saying that having a history at Michigan and being a "Michigan man" was not a prerequisite for getting the job.

Dazed And Blue Michigan will start 2015 with its third coach since 2008. Quite a difference from the stability the program once enjoyed. 1969-07 2008-15 Coaches 3 3 Win pct .776 .523 Conf titles 21 0 Losing years 0 3 -- ESPN Stats & Information

"I want to get rid of the word 'Michigan Man,' " said Hackett, who stepped into temporarily run the athletic department one month ago. A former center at Michigan under Bo Schembechler and CEO of office furniture company Steelcase, Hackett plans to be the man who will hire Hoke's replacement.

Hoke, who is owed a $3 million buyout, earned the title of a Michigan Man when he told reporters he would've walked to Ann Arbor to accept the Wolverines' job when he was introduced as the head coach four years ago. He served as an assistant at Michigan from 1995 until 2002, when he left to take the head coaching job at Ball State.

With his Michigan tie, Hoke was hired to stabilize the program following the tumultuous tenure of Rich Rodriguez. Rodriguez, now the head coach at Arizona, was named the Pac-12 Coach of the Year on Tuesday.

The Wolverines' underwhelming performance also led to the resignation of former athletic director Dave Brandon, the man who had hired Hoke.

Hoke won 11 games and the Sugar Bowl in his first season as Michigan's head coach, but his team's trended steadily downward in the three years that followed. The Wolverines' loss to rival Ohio State last weekend dropped their record to 5-7 and ended their first losing season since 2009. Michigan is just 1-10 in their last 11 games against the Buckeyes and have not won a Big Ten title since 2004.

Information from The Associated Press and ESPN.com's Darren Rovell contributed to this report.