The news was first reported by NFL Network.
Amendola is the second wide receiver to commit to signing with the Dolphins on Tuesday. Wide receiver Albert Wilson committed to signing a three-year, $24 million deal with the team earlier Tuesday.
Both players will help to fill the void created when Jarvis Landry is traded to the Cleveland Browns this week. The Dolphins placed their franchise tag on Landry after he led the NFL with 112 receptions last season, and agreed to trade him to Cleveland for two draft picks last week.
Amendola, 32, had accepted a pay cut in each of the past three offseasons to remain with the Patriots, and has developed a well-earned reputation as a clutch performer in the playoffs.
Amendola said in late February at a speaking event in Rhode Island, "I'm a free agent this year, so let's say -- the unknown. We'll see what happens. I definitely want to be here [in New England]. To tell you the truth, I don't want to leave. But it's a business. I've learned that."
In the final episode of the "Tom vs. Time" docuseries, quarterback Tom Brady calls up tight end Rob Gronkowski on the ride home from the AFC Championship Game, and Gronkowski asks Brady, "How does Danny get so good in the playoffs?"
Amendola played 49.9 percent of the offensive snaps in 2017, a result of the team losing receiver Julian Edelman to a torn ACL in the preseason and Chris Hogan missing seven regular-season games with a shoulder injury. The Patriots have managed Amendola's health carefully in recent years to preserve him for the homestretch and playoffs, but 2017 required him to take on a larger load, and he responded.
Edelman and Brady wished Amendola the best in Instagram posts.
Amendola finished with 61 catches for 659 yards and two touchdowns in the regular season, while adding 26 catches for 348 yards and two touchdowns in the playoffs. He was also the team's primary punt returner in 2017.
While the Patriots wanted him to return in 2018, their projected role for him might not have been as large as what others were willing to offer, which also ties in to what type of contract the Patriots might have been willing to offer.
ESPN's Mike Reiss contributed to this report.