ESPN's Chris Mortensen first reported the switch.
“I’m thankful and very excited for the opportunity to start," Allen told reporters. "I’m just looking to do whatever is necessary to get a win.”
Peterman secured the top spot on the depth chart after completing 80.5 percent of his 41 preseason attempts with three touchdowns and one interception.
The 24-year-old University of Pittsburgh product was an unmitigated disaster as the Bills suffered a 47-3 blowout loss to the Baltimore Ravens in the season opener, though. He went 5-of-18 for 24 yards with no scores and two picks before getting replaced by Allen in the second half.
Peterman's poor outing harked back to his first career start against the Chargers last November when he tossed five interceptions in the first half.
"Obviously it wasn't a good showing," Peterman told reporters after getting benched during the Ravens game. "We've got to do a lot better, starting with me."
Allen, the seventh overall pick in the 2018 NFL draft, didn't play much better after making his NFL debut in relief during Week 1. He completed six of 15 throws (40 percent) for 74 yards.
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Bills head coach Sean McDermott said there are "a lot of things" that go into deciding whether to hand the offensive keys to the rookie on a full-time basis, including the California native's development.
"I have a lot of confidence in Josh, and a lot of confidence in this football team, and we'll continue to grow and continue to develop," he said. "We've got a lot of young players on this football team."
Ultimately, Buffalo features one of the league's least talented rosters and is unlikely to contend for a playoff spot one season after ending its 17-year postseason drought.
Combine that with the fact that Peterman has already shown he's not the long-term answer under center and there's little reason for the Bills to start anyone other than Allen. It's best to let him go through growing pains in a low-pressure environment.
Expectations should be kept within reason since the team doesn't feature the big-play weapons that best fit Allen's rocket-armed skill set. But the front office and coaching staff will still hope to see legitimate progress from the new face of the franchise over the next few months.