Terms were not disclosed but a source said the deal is for one year.
Wynn was selected in the first round of the 2018 NFL draft by the Patriots. He started four seasons at left tackle in New England before switching to right tackle in 2022.
Dolphins general manager Chris Grier said in March that the expectation is for Austin Jackson to start at right tackle, but the position is not quite solidified. Jackson played just two games at right tackle last season, with an ankle injury sidelining him for the other 15.
Miami drafted Michigan tackle Ryan Hayes in the seventh round of this year's draft, but Jackson and Wynn will likely compete for the right tackle job this summer. Ogbuehi also should enter into the competition with Wynn and Jackson.
Wynn also offers the flexibility to play left tackle if needed, as Pro Bowler Terron Armstead has missed three or more games in nine of his 10 NFL seasons.
Wynn, 27, played in 43 of a possible 82 regular-season games for the Patriots, with various injuries keeping him on the sideline.
The Patriots hoped for different results when they picked up his $10.4 million fifth-year option for the 2022 season, but Wynn's time with the franchise fizzled out as he appeared in just nine games (seven starts) due to a hip injury.
The Patriots had envisioned Wynn would become a stalwart at left tackle, much as Matt Light (2001-2011) did in the first half of Bill Belichick's tenure as head coach. Just like Light, the 6-foot-2, 310-pound Wynn doesn't have the prototypical physical makeup for the position -- which is why some teams envisioned him as a better fit at guard -- but his athleticism rates highly.
Wynn didn't attend voluntary offseason workouts in 2022, and when training camp began, the coaching staff flipped him from left tackle to right tackle. Wynn, who was penalized eight times in 2022, didn't seem to fully embrace the switch.
"Playing left all the time and then having to flip, that's like you being right-handed and then you're trying to write with your left hand," Wynn said before training camp. "But you get used to it the more you work at it."
Ogbuehi, a first-round pick by the Cincinnati Bengals in 2015, has primarily played right tackle during his eight-year NFL career. Besides the Bengals and Jets, he has spent time with the Jacksonville Jaguars, Seattle Seahawks, Baltimore Ravens, Tennessee Titans and Houston Texans.
ESPN's Mike Reiss contributed to this report.