Brian is the son of former NFL Quarterback Bob Griese, who spent his entire career with the Miami Dolphins.

After he was redshirted in 1993 and limited to placeholding duties in 1994, Griese took over as the starting quarterback after Scott Dreisbach was injured five games into the 1995 season.

At the beginning of the 1996 season, Dreisbach regained his starting job and Griese returned to the bench, serving as the team's pooch punter.

However, after Dreisbach struggled, Griese replaced him at halftime against Ohio State, where he led the Wolverines to another upset victory over the Buckeyes, 13–9.

Along with Heisman Trophy winner Charles Woodson, he led the Wolverines to an undefeated season and a share of the national championship.

Griese was selected as the MVP of the 1998 Rose Bowl, passing for 251 yards and three touchdowns in Michigan's win over Washington State.

Though he fared better than Rex Grossman during the 2006 preseason, coach Lovie Smith decided to keep Griese as the Bears’ second-string quarterback.

In a game against the Detroit Lions, Griese completed six of nine passes for 51 yards, which set up several game-winning Robbie Gould field goals.

Smith called on Griese to relieve a struggling Grossman for the second half of the final regular season game against the Green Bay Packers.

[2] In his first outing as a Bears starter, Griese threw two touchdowns and three interceptions in a losing effort against the Detroit Lions.

[3] The next week, he led the Bears on a game-winning drive against the Philadelphia Eagles, in which he called the plays due to a headset failure.

He also started the following week, and again despite throwing 3 interceptions, he completed 15 of 30 passes for 149 yards, 1 touchdown, and lead the Bucs to a victory over the Green Bay Packers 30–21.

[9] From 2020 to 2022, Griese joined the booth for Monday Night Football, working alongside Steve Levy and Louis Riddick.

Griese was a member of the Phi Gamma Delta fraternity and received his bachelor's degree in an individualized concentration from Michigan in 1997.

Griese is founder and board president of Judi's House, a children's grief support center in Denver, Colorado.

He also remains involved with the From the Heart Organization, a relationship that dates back to his playing days in Ann Arbor when he would visit Mott every week.

These awards recognize Big Ten football players that have achieved success in the areas of leadership and humanitarianism after their college careers have ended.

[14] Brian and his father, Bob Griese, became the first father-and-son duo in NFL history to both win a Super Bowl.