Moore, 28, was the backup to rookie Ryan Tannehill last season. Moore appeared in 10 games, but he didn't start any. He was 11-for-19 for 131 yards and a touchdown. He didn't throw an interception in his limited time on the field.
Details of the contract are unknown.
Before the Dolphins drafted Tannehill, Moore had a solid season for Miami in 2011. He started 12 games and led the team to a 6-6 record. He completed 60 percent of his passes for 2,497 yards and 16 touchdowns. He threw nine interceptions and was sacked 36 times.
Moore was an undrafted free agent out of Oregon State in 2007.
Moore was in a quarterback competition with Tannehill before the start of the 2012 season, but the team decided to hand the keys over to the rookie. Tannehill, who was the No. 8 selection in last year's draft, completed 58 percent of his passes for 3,294 yards and 12 touchdowns last season. He threw 13 interceptions.
With the Arizona Cardinals needing to address the quarterback position, Moore had been mentioned as a possible target and solution. With his return to Miami, Arizona now will have to look to other options.