The Dallas Cowboys have agreed to terms with Mike McCarthy to be their next head coach ... just roughly 15 hours after they officially canned Jason Garrett from the role.

Of course, the hire -- reported by FOX Sports' Jay Glazer -- was immediately hit with backlash ... especially considering the 'Boys only looked at McCarthy, Marvin Lewis and Jeff Fisher for the role.

But, Mike does at least come to Dallas with a nice resume ... the former Green Bay Packers head man was 125-77-2 in his 13 years with the Pack -- including a win in Super Bowl XLV.

McCarthy, though, received plenty of criticism for his time in Green Bay ... with most down on the guy for only winning one ring with Aaron Rodgers under center.

In fact, Mike was canned by the Packers last season after he and A-Rodge reportedly rifted on and off throughout their final years together in Wisconsin.

McCarthy will become just the 8th head coach Jerry Jones has hired since he bought the team back in 1989 ... joining a list that includes Jimmie Johnson, Barry Switzer, Chan Gailey, Dave Campo, Bill Parcells, Wade Phillips and Garrett.