He played college football for the Pittsburgh Panthers following a stint with the Tennessee Volunteers and was selected by the Buffalo Bills in the fifth round of the 2017 NFL draft.
Peterman struggled early in the NFL, throwing five interceptions during the first half of his starting debut and posting a 0.0 passer rating in the 2018 season opener.
Peterman was rated as a four-star recruit and committed to the University of Tennessee to play college football under head coach Derek Dooley.
[7][8] Peterman made his collegiate debut in a home game at Neyland Stadium against Austin Peay in relief of Worley in a 45–0 victory.
He played in seven games and made one start, which came against #4 Alabama at Neyland Stadium, after Worley was injured in the 34–3 loss to #3 Ole Miss.
[23][24] Under new head coach Pat Narduzzi, Peterman entered the season as the backup to Chad Voytik, but replaced him as the starter after two games.
[26] He kept the starting job for the rest of the year, completing 193-of-314 passes for 2,287 yards, 20 touchdowns, and eight interceptions as the Panthers finished with an 8–5 record.
[34] During Senior Bowl practices, Peterman impressed scouts and media in attendance after he displayed his decent size, accuracy, mobility, and his powerful arm.
He met with representatives from the New Orleans Saints during the week and was praised by NFL analysts Daniel Jeremiah and Charles Davis.
[35] On January 28, 2017, Peterman played in the Senior Bowl and completed 16 of 23 pass attempts for 153 yards and a touchdown during the North 16–15 loss to the South.
Peterman finished fifth among quarterbacks in the three-cone drill, seventh in the 40-yard dash and tied for sixth in the vertical jump and short shuttle.
[47][48] On November 15, 2017, Peterman was named the Bills' starting quarterback for the team's Week 11 game against the Los Angeles Chargers due to Taylor's struggles.
[53] On January 7, 2018, Peterman entered the Bills' Wild Card Round game against the Jacksonville Jaguars with 1:43 remaining in the 4th quarter after Taylor suffered a concussion.
Peterman competed with rookie first-round draft pick Josh Allen and free-agent signing A. J. McCarron for the starting quarterback position.
[56][57][58] On September 3, 2018, the Bills named Peterman their opening day starter over Allen after trading McCarron to the Oakland Raiders.
[59] Starting in Week 1 against the Baltimore Ravens, Peterman completed 5–18 passes, for 24 yards, throwing two interceptions and not leading the team to a first down until the third quarter.
[63] After Allen was injured against the Houston Texans and with Anderson inactive, Peterman entered the game and threw a touchdown to Zay Jones to put Buffalo in the lead.
[64] On October 17, 2018, Bills head coach Sean McDermott confirmed that Anderson would start Week 7 against the Colts with Allen ruled out.
[89][90] On December 3, 2022, Peterman was signed to the active roster after Siemian was placed on injured reserve, becoming Fields' primary backup.
[91] He made a relief appearance in place of Fields against his old team, the Bills, during the waning moments of a 35–13 defeat on Christmas Eve.
[92] On January 4, 2023, Peterman was named the starter for the Week 18 matchup against the Minnesota Vikings, replacing Justin Fields who was ruled out for a sore hip.
[95][96] He was named the second-string option behind starter Justin Fields and ahead of undrafted rookie Tyson Bagent, beating out veteran P. J. Walker for the role.