The 34-year-old left the Catalan giants at the end of the campaign after 11 seasons, having joined from Valencia in 2012.
Alba will now embark on his new chapter, and link up with former Barca teammates Messi and Busquets in Florida.
The full-back made 459 appearances for the Catalan giants, netting 27 goals, whilst producing 99 assists.
He also got his hands on six LaLiga titles, five Copa del Reys and a Champions League triumph.
Inter Miami owner, Jorge Mas, said: "Jordi Alba will sign today. Messi will debut on Friday."
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Recent reports have suggested all three players could be joined by another former Barcelona star in Luis Suarez at David Beckham's MLS franchise.
Manchester United legend Wayne Rooney, the boss of DC United, also reckons the Uruguayan could soon terrorise defences.
"Messi comes, Busquets comes, you hear that [Luis] Suarez is coming, Jordi Alba's coming," he said in a recent interview.
"So for Inter Miami it's about to be very interesting to see how they fit all of them in. But for the league I think it's huge, it is."
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However, Mas has since played down the rumours, saying: "Luis Suarez is a Gremio player. He has a contract. We understand the close relationship that he has with Lionel, Busquets and Alba.
"They played together at Barcelona. There's been a lot of talk about Luis Suarez coming to Inter Miami. We haven't held direct talks with Gremio or with Suarez.
"I don't know how Luis Suarez can leave Gremio. But if he does we are free to talk to Luis and bring him to Inter Miami. That possibility would be there."