The MLS side has announced the arrival of the ex-Spain international on its social media accounts.
Busquets' contract with Barca expires at the end of June and, after announcing his decision to end his 18-year stay at Spotify Camp Nou, he has been mulling over offers from the United States and Saudi Arabia.
Sources have told ESPN that Busquets will put pen to paper on a two-and-a-half-year deal pending the final revision and signing of contracts.
Busquets, 34, held negotiations with Saudi sides Al Nassr and Al Hilal in recent weeks but opted for Miami's offer, which sources say was financially inferior, having previously spoken of his desire to play in the U.S.
He will be reunited in South Florida with seven-time Ballon d'Or winner Messi, who announced his intention to move to MLS earlier this month following the expiry of his contract with Paris Saint-Germain.
Busquets and Messi spent 13 years playing alongside each other in Barca's first team before Messi's move to Paris in 2021. The two have remained close friends since.
Busquets made 722 appearances for Barca in total, winning nine league titles and three Champions Leagues during that time.
He has also been capped 143 times by Spain, winning the World Cup in 2010 and the European Championship in 2012 before announcing his retirement from international football after last year's World Cup in Qatar.
Busquets and Messi could yet be joined in Miami by Alba, who reached an agreement with Barca last month to end his contract -- which was due to expire in 2024 -- one year early.
The left-back is also courting interest from Atletico Madrid, Inter Milan and clubs in Saudi Arabia, with sources telling ESPN he will take some time with his family following the conclusion of the Nations League before making a final decision.
Alba's desire to represent Spain in next summer's European Championship, coupled with the fact that his partner is due to give birth to their third child in July, could influence his next move.