Tampa Bay received two second-round picks -- Nos. 53 and 56 -- along with the 12th overall pick from Buffalo, which also acquired the 255th pick.
The Broncos and Bills had agreed to a deal for some of the afternoon, per ESPN's Adam Schefter, but ultimately when defensive end Bradley Chubb was still available at No. 5, Denver didn't want to do it, leading to Buffalo trading with Tampa Bay instead.
But more importantly, the Bills landed who they hope is their quarterback of the future in Allen, who has endured a firestorm of scrutiny in the last 24 hours after racially insensitive tweets he sent while in high school were made public Wednesday night.
When asked whether the Bills took a risk in selecting him, Allen told ESPN that he is "going to make (the Bills) look like the smartest people out there."
Allen also was asked whether he will address the content of the tweets with his new Bills teammates.
"I don't have to, but I probably will," he told ESPN. "I want them to know that I'm going to work to be the best teammate possible."
Allen, who figures to compete with AJ McCarron for the starting job with the Bills, is the highest-selected quarterback in Bills history. He becomes the fourth quarterback selected in the first round by Buffalo in the common draft era, joining Jim Kelly (No. 14 in 1983), J.P. Losman (No. 22 in 2004) and EJ Manuel (No. 16 in 2013.
The Bills went 9-7 last season and reached the playoffs for the first time since 1999.