ESPN's Adam Schefter first reported the news on Monday.
Griffey, the son of baseball legend Ken Griffey Jr., was released by the Indianapolis Colts and cleared waivers in July. He was on the injured reserve list prior to the transaction and reached a settlement with the team.
He was signed as an undrafted free agent in May.
Griffey spent his college career at Arizona, totaling 79 catches for 1,241 yards and six touchdowns in four seasons. He finished with 382 yards and two scores during his senior year, earning him an honorable mention spot on the All-Pac-12 team.
Although he was also selected by the Seattle Mariners in the 2016 MLB draft, the pick was more of a nice gesture for his father considering Trey hasn't played competitive baseball since before high school.
The Dolphins have several established players in the receiving corps between Jarvis Landry, DeVante Parker and Kenny Stills, but there are still spots up for grabs at the end of the depth chart. With seventh-round pick Isaiah Ford dealing with a knee injury, Griffey has a chance to earn a roster spot for the 2017 season.