Wilson set career-highs in catches (42), yards (554) and touchdowns (3) previous year with the Kansas City Chiefs.
The Dolphins traded Jarvis Landry, putting them in the market for a veteran receiver.
He was Tom Brady's main target during the Pats run to the Super Bowl previous year, reeling in 26 passes for 348 yards and a pair of touchdowns, including 8 for 152 in the big game.
The signing can become official Wednesday when the new league year begins. He also attended Port St. Lucie High School in Florida. Reserve safety Walt Aikens discussed re-signing with Miami and is likely to reach a deal, a person familiar with the negotiations said. Landry averaged 8.8 yards per reception, while Wilson averaged 13.2 yards per catch on his 42 grabs. Last season, Stills had 58 catches for 847 yards and six scores after re-signing with the franchise in the offseason on a four-year, $32 million pact.
His departure clears $5.5 million in cap space for Miami.
Timmons went AWOL on the eve of last year's opener, was briefly suspended and played poorly when he returned.