Jones' deal is for five years and $82.5 million, including $57 million guaranteed, a source told ESPN's Adam Schefter. The agreement includes $40 million in the first two years, the source said.
The NFL Network first reported that Dolphins and Jones had reached an agreement.
The Dallas Cowboys drafted Jones in the first round in 2015. He moved from safety to cornerback in 2018 and was a Pro Bowl selection that season, despite not intercepting a pass. He started 14 of the 15 games in which he appeared last season after having offseason hip surgery.
The surgery caused him to miss the offseason program and training camp. Jones also missed the final game of the season because of an ankle injury suffered in practice.
If there is a knock on Jones, it is his inability to take the ball away. He has gone 40 games without an interception and has just two for his career. Since the 1970 merger, Jones and Johnathan Cyprien are the only defensive backs to start at least 70 games during their first five seasons and record fewer than five interceptions.
But Jones does not give up much. Opposing quarterbacks completed just 53% of their passes directed at Jones in 2019, and he gave up three touchdowns.
He started 11 games at cornerback or safety as a rookie. In 2016 and 2017, Jones started every game at safety. After returning to cornerback in 2018, he had a career-best 15 pass deflections to go along with 76 tackles.
Without Jones, the Cowboys will have to look for a replacement either in the draft -- potentially with their first-round pick -- or via free agency, where Anthony Brown could return on a short-term contract. The Cowboys have Chidobe Awuzie and Jourdan Lewis under contract for 2020, but both players are set to be unrestricted free agents in 2021.
The Dolphins also agreed to terms with safety Clayton Fejedelem on a three-year contract, according to his agent, Mike McCartney. Fejedelem was a special-teams standout and reserve safety for the Cincinnati Bengals for the past four seasons. With Dolphins special-teams ace Walt Aikens now a free agent, Fejedelem could end up replacing him.
ESPN's Cameron Wolfe and Todd Archer contributed to this report.