The 31-year-old is expected to sign a two-and-a-half year deal with David Beckham's MLS franchise and will move to the United States once his contract expires at West Bromwich Albion this summer.
Gibbs moved to the Hawthorns from Arsenal in August 2017 for £7 million and has made 100 appearances.
The left-back, who has amassed 10 England caps, is West Brom's highest-paid player on £70,000-a-week and the club are looking to reduce their wage bill with relegation to the Championship increasingly likely. They are 10 points adrift of 17th-placed Newcastle United.
The paperwork is yet to be signed but all parties are confident the deal will go through, meaning Gibbs will arrive midway through new manager Phil Neville's first season in charge.
Neville is aiming to improve on a disappointing 10th place finish in the Eastern Conference in Miami's inaugural campaign and has already signed Ryan Shawcross from Stoke and Brazilian midfielder Gregore from Bahia.
"In terms of the roster we definitely want to add two or three more players, that's imperative for us to have a good season," Neville said last week.
"We're working really hard, [chief soccer officer] Chris Henderson is doing a really good job. ... I do expect there to be one, two or maybe three more additions, but we'll have to see."