The team later announced the move.
Garrard said he expects to compete for the starting job with incumbent Matt Moore and perhaps another quarterback the Dolphins acquire.
"They didn't say for sure they were bringing another guy in, but they said it's a possibility, whether in the draft or whatever," Garrard said in a phone interview with the Associate Press.
For now, Garrard and Moore are the only contenders.
"It's going to be a great competition, and I'm all about that," Garrard said. "I'm going to do my best to make sure it's me on opening day."
A league source told NFL Network insider Jason La Canfora that Garrard's deal is for one year.
The Dolphins missed out on Peyton Manning and Matt Flynn, who chose the Denver Broncos and Seattle Seahawks, respectively. Alex Smith visited Miami on Sunday, but with Garrard now in Miami, Smith could return to San Francisco, where he has spent his entire NFL career.
Garrard, a starter for the Jaguars from 2005 to 2010, didn't play last season. He was released five days before the opener, then underwent back surgery in October.
The Dolphins offered Garrard a contract last season after his release, but the season-ending surgery on his herniated disc quelled talks between the two sides.
Garrard compiled a 39-37 record with the Jaguars in his time with the team. In his last season in Jacksonville, he threw for 2,734 yards with 23 touchdowns and 15 interceptions.
He made the Pro Bowl in 2009 after throwing for 3,597 yards with 15 touchdowns and 10 interceptions.
The Associated Press contributed to this report.