He earned All-American honors playing college football with the Purdue Boilermakers before being drafted in 1967 by the Dolphins of the AFL.

In his junior year at Purdue in a game against the top-ranked Notre Dame, Griese completed 19 of 22 passes as he led the Boilermakers to an upset win.

Purdue finished second in the Big Ten in 1966, and he led the school's first appearance in the Rose Bowl, where they defeated USC 14–13.

[19] On December 11, 2014, the Big Ten Network included Griese on "The Mount Rushmore of Purdue Football", as chosen by online fan voting.

[21] While he never put up huge numbers, his leadership played an important role in helping the Dolphins compete in three consecutive Super Bowls, winning the latter two contests.

When Stofa broke his ankle in the first quarter of the first game of the 1967 season, Griese stepped in and led the Dolphins to a 35–21 victory against the Denver Broncos.

Dolphin owner Joe Robbie brought in Don Shula from the Baltimore Colts in 1970,[23][24] and the team's personality and fortunes turned quickly.

In the fifth game of the season, Bob Griese was tackled hard by Deacon Jones and Ron East of the San Diego Chargers, and went down with a broken leg and dislocated ankle.

[31] Earl Morrall, fresh off the waiver wire from Shula's former team, the Baltimore Colts, guided the Dolphins through the rest of the regular season, and maintained an unbeaten record in the process.

[32] As the playoffs began, the Dolphins were not as strong as they needed to be to go deep into the postseason, barely winning against the Cleveland Browns, a team that they should have beaten easily.

Griese won back the starting spot in the fifth game of the season, but was tackled hard by Mike Ozdowski of the Baltimore Colts.

The injury eventually led to Griese's decision to retire from the game at age 35; he was elected to the Pro Football Hall of Fame in 1990.

Robbie elected to ask Griese to stay on for another year as assistant coach, which he did for the 1981 season, helping Strock and the young Woodley as they teamed to become the famous “Woodstrock.” After the year ended, he decided that he did not like the hours required to be an assistant coach, hoping to devote more time to his family, yet he still enjoyed being part of the game.

(Sources for Pro Football Career found in Undefeated, by Bob Griese, 2000, and The Winning Edge by Don Shula, 1974.)

The Miami Dolphins had the highest winning percentage in all professional sports in the 1970s, and Bob Griese was its starting quarterback throughout the decade, except when he was injured for several games in 1972, 1975, and 1978.

The Dolphins retired his number 12 during a Monday Night Football game in 1985, telecast on ABC, the network which would prominently be featured in his post-football career.

In 1987, Griese was hired by ABC Sports, where he began to provide color commentary for college football games.

But when they decided to give it a try, Bob remained as impartial and professional as he could be, even referring to his son as “Griese,” rather than Brian, and pointing out errors when he felt necessary.

Brian was named MVP of the game, leading his Wolverines to an undefeated season and the national championship title with their Rose Bowl victory.

Bob and Brian later wrote a book, entitled Undefeated (ISBN 0-7852-7021-3), which discussed not only their football connection, but also their love for Judi.

Brian became a professional quarterback and broadcaster himself, playing for the Denver Broncos and Tampa Bay Buccaneers, and later commentating games for ESPN and ABC.

[42] Griese married Purdue classmate Judi Lassus in June 1967,[43] following their graduation, and they had three sons: Brian, Jeff, and Scott.

[46] In 2006, Griese made an appearance on the game show, Wheel of Fortune: he won the $100,000 grand prize and donated his $114,310 total winnings to Judi's House.