Cleary was born in Carbonear, Newfoundland, the location of the area's only hospital, and was raised in Harbour Grace, in a section of the town called Riverhead.

Cleary played his final year of major junior hockey during 1997–98, leading the OHL playoffs in assists (17) and points (23).

[3] Just one year removed from junior hockey, Cleary was dealt to the Edmonton Oilers as part of a package that landed Boris Mironov in Chicago.

[6] On July 1, 2008, Cleary brought the Stanley Cup back to his hometown of Harbour Grace, Newfoundland for a Canada Day celebration that included a parade and a concert.

In addition to receiving extensive local radio airplay, the song appeared on CBC Television and a Fox Sports Detroit special.

[7] In the 2009 Stanley Cup playoffs on May 14, 2009, Cleary scored the tie breaking, Western Conference semi-final series winning goal for the Detroit Red Wings against the Anaheim Ducks with three minutes left in game seven.

Cleary scored five goals against his former team in a 4-1 series win clinching the Western Conference title before succumbing to the Pittsburgh Penguins in seven games in a rematch of the previous Stanley Cup Finals.

[10] On September 23, 2016, Cleary signed a one-year contract with the Grand Rapids Griffins of the American Hockey League (AHL).

[11] During the 2016–17 season, Cleary did not feature in a game for the Griffins instead serving as an unofficial player/coach role in mentoring the younger players within the Red Wings organization.