The Browns will give up a third-round pick, No. 65 overall, for Taylor, according to the source.
The trade for Taylor came on the same day Cleveland agreed to acquire wide receiver Jarvis Landry from the Miami Dolphins, a source told Schefter. In another trade, the Browns sent quarterback DeShone Kizer to the Green Bay Packers for cornerback Damarious Randall, and as part of the deal the teams will swap picks in both the fourth and fifth rounds of this year's draft, a source told ESPN.
Taylor's acquisition would seem to take the Browns out of the free-agent quarterback market. It had been expected that the Browns would be interested in Cincinnati's AJ McCarron, but McCarron likely will not sign with a team that already has Taylor.
The Browns were interested in Taylor a year ago, but he agreed to stay in Buffalo with a new contract just before the start of free agency. If he starts the opener, he will be the 29th starting quarterback for the Browns since 1999.
Taylor joins a Browns team that lacked a veteran and turned to Kizer for 15 starts as a rookie last season. Kizer was the Browns' second-round pick in the 2017 draft and won the starting job in a training camp competition with Brock Osweiler and Cody Kessler. Coach Hue Jackson spoke glowingly of Kizer when he named him the starter and stood by his talent throughout the season.
But Kizer struggled with accuracy and interceptions. His 6.1 percent interception rate through the first five games was far and away the highest in the league and led to his being pulled from two games and benched for another. He finished the season with a league-high 22 interceptions.
Kizer's completion percentage of 53.6 percent was well short of the 60 percent target he had said he needed. But he finished the season finale with 314 yards passing and 61 yards rushing against the Pittsburgh Steelers as he made a frantic attempt to get the Browns their first win.
When the season ended, Kizer lamented the fact he would be remembered as the quarterback of an 0-16 team. After the season, Jackson said Kizer would be back and would compete for the starting spot. His trade is a bit of a surprise in that the Browns never gave any indication they were eager to move him.
Even after Friday's deals, the Browns still have the Nos. 1, 4, 33, 35 and 64 picks in this year's draft. The Bills now own two picks in each of the first three rounds: Nos. 21, 22, 53, 56, 65 and 96.
The trade is expected to clear $10.44 million in 2018 cap space for the Bills, who had Taylor under contract through next season at $18.08 million. The Browns will inherit a one-year deal for Taylor that includes a $10 million base salary ($1 million of which is fully guaranteed) and a $6 million roster bonus due March 16.
Friday's trade leaves 2017 fifth-round pick Nathan Peterman as the only quarterback under contract for the Bills.
Taylor, 28, compiled a 23-20 record in 43 starts for the Bills since 2015. After he won the Bills' starting quarterback competition in 2015 and made the Pro Bowl, Taylor's production declined in each of the past two seasons.
He averaged 6.66 yards per pass attempt and threw for 14 touchdowns in 2017, short of his career highs set in 2015 of 8.0 yards per attempt and 20 touchdowns. He also compiled an 89.2 passer rating and a 56.4 Total QBR, down from his career-high 99.4 passer rating and 65.3 Total QBR in 2015.
The Bills signed Taylor to a five-year contract extension before the 2016 season that could have allowed him to earn $90 million. After Taylor posted a losing record in 2016, he accepted a renegotiated contract last year that eliminated the final three seasons and included a significant pay cut.
Taylor began last season with a 5-4 record but was benched by first-year coach Sean McDermott after back-to-back losses to the New York Jets and New Orleans Saints in which the Bills were outscored 81-31.
Peterman threw five interceptions in the first half of the Bills' first game after Taylor was benched, leading McDermott to hand the starting job back to Taylor for the remainder of last season.
Taylor completed 17 of 37 passes for 134 yards, one interception and a 44.2 passer rating before leaving with a concussion in the fourth quarter of the Bills' wild-card playoff loss to the Jacksonville Jaguars.
He ends his Bills career as the franchise's all-time leader in passer rating (92.5) among quarterbacks to have started at least one game. His 1,575 rushing yards are also the most in franchise history among quarterbacks and are the second most in the NFL since 2015 by a quarterback behind Cam Newton (1,749).
In Damarious Randall, the Packers' 2015 first-round pick, the Browns get a cornerback who has been a mix of promise (2015), disappointment (2016) and wild inconsistency (2017).
Last season, Randall posted a career-high and team-leading four interceptions but also got benched and was sent to the locker room in the middle of a game against the Chicago Bears, and then he couldn't get on the field for the final two games because of a knee injury. Randall also underwent hand surgery last month but expects to make a full recovery.
The Packers stuck by Randall after his benching, even though there was some serious discussion within the organization about whether to cut him. He played some of his best football in the games that followed, with three of his four interceptions coming in the three games that immediately followed his benching.
Green Bay used its top overall pick last offseason on cornerback Kevin King, who was the 33rd overall pick, a selection the Packers got in a draft-day trade with the Browns.
ESPN's Rob Demovsky and Mike Rodak contributed to this report.