Hill, who is from Youngstown, Ohio, had a breakout season for the Los Angeles Rams in 2020, starting all 16 games for the first time in his six-year career. He had three interceptions and three defensive touchdowns for the NFL's top-ranked defense.
In a Week 12 loss to the San Francisco 49ers, Hill returned a fumble recovery 20 yards for a touchdown. The following week, he intercepted a pass by Arizona Cardinals quarterback Kyler Murray and took it 35 yards for a score. He had another TD against the Cardinals in the regular-season finale, intercepting backup quarterback Chris Streveler and sprinting 84 yards for a touchdown.
He also had 10 passes defended for a secondary that included All-Pro cornerback Jalen Ramsey.
The Browns have already bolstered their secondary in free agency, signing safety John Johnson III, who also came over from the Rams.
Hill moved into a starting position in 2019 in Week 7 after Aqib Talib was placed on injured reserve because of a knee injury. He finished the season with two interceptions and eight passes defended, earning him the starting job going into 2020.
Hill, who turns 30 in August, signed with the Cincinnati Bengals in 2015 as an undrafted free agent from Oregon. He appeared in three games his rookie season with the Bengals. The Rams acquired Hill off the waiver wire at the end of the 2015 season.
In five seasons in L.A., Hill had seven interceptions, 29 passes defended, a sack, a forced fumble and three fumble recoveries.
ESPN's Lindsey Thiry contributed to this report.