The one-year deal is worth $10 million, plus up to $3 million in incentives, a source told Schefter.
In May, Cutler had retired from the NFL and was hired by Fox Sports as a game analyst.
"We loved our time working with Jay and wish him the best back on the field this year with the Dolphins," Fox said in a statement Sunday.
Dolphins coach Adam Gase has played a significant role in convincing Cutler of the reasons he should play for the Dolphins, sources told ESPN's Jeff Darlington. Miami also raised its monetary offer, sources close to the situation said.
On Monday, Gase confirmed that Cutler will not play in Thursday's preseason opener against the Atlanta Falcons.
As of Saturday, Cutler was reluctant about a possible return to football, although he hadn't made any decision with certainty. Aware of his reluctance, but after a day of no direct communication with Cutler, Gase was eventually able to talk to him.
The Dolphins targeted Cutler because of the likelihood that starting quarterback Ryan Tannehill will undergo surgery to repair stretched ligaments in his left knee.
Cutler, 34, started 15 games in 2015 with Gase as his offensive coordinator, throwing for 3,659 yards with 21 touchdowns and 11 interceptions. He completed 64.4 percent of his passes.
Last season, Cutler played in just five games because of thumb and shoulder injuries. He suffered a torn labrum in his right throwing shoulder and underwent surgery in December.
Before the Dolphins' agreement with Cutler, veteran backup Matt Moore had been poised to take over for Tannehill as the starting quarterback. Moore turns 33 next week and has 28 starts in 10 seasons. Last year he helped the Dolphins clinch their first postseason berth since 2008, going 2-1 as a starter to end the regular season before a first-round playoff loss at Pittsburgh.
Gase gave Moore only a tepid endorsement Friday, saying: "Right now Matt is our quarterback.''
The Associated Press contributed to this report.