To make room for the move, Miami placed former starting linebacker Koa Misi on injured reserve. Misi is still recovering from a neck injury that forced him to miss 13 games last season.
Verner, 28, who started 70 career games for the Tennessee Titans and Tampa Bay Buccaneers, will have a chance to compete for playing time against younger corners Xavien Howard and Tony Lippett, and opposite starter Byron Maxwell. Verner's best season was in 2013, when he had a career-high five interceptions and made the Pro Bowl.
The Dolphins were looking for veteran depth in the secondary before training camp and worked out several cornerbacks in recent days.
"So many people tell me you can't find enough corners," Dolphins coach Adam Gase said earlier Tuesday before signing Verner. "So we're checking guys out, but we do that quite a bit with a lot of positions."
Misi underwent surgery on his neck in the offseason. He accepted a pay cut earlier this season to stay with the team.
The Buccaneers released Verner on Feb. 23. He started just three games during the 2016 season.
The arrival of cornerback Vernon Hargreaves, who was drafted 11th overall last year, and the signing of Brent Grimes had signified that the Buccaneers would likely part ways with Verner under defensive coordinator Mike Smith.
Verner's best game last season came when, just 48 hours after his father died of a heart attack, he recorded an interception and two pass breakups in the Bucs' 14-5 win over the Seattle Seahawks.
ESPN's Jenna Laine contributed to this report.