Alba is set to become the third ex-Barca player to sign for the MLS side this summer after Messi and Sergio Busquets both penned deals at the club.
The Spain captain called time on his career at the Nou Camp at the end of last season after ten years at the club, winning six La Liga titles and the Champions League.
Alba - who will sign a two-and-a-half-year deal - joins his former teammates in South Florida under the guidance of former Barcelona boss Tata Martino.
Previously, reports surfaced that Messi and his pals had formed a pact to reunite in the Saudi Pro League, once Messi had ended his association with Paris Saint-Germain.
But Messi refuted the claims telling Sport: "It's another of the things they said, that I was going with Busi [Sergio Busquets] and Jordi [Alba] to Saudi Arabia, that we had everything arranged.
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"I was obviously aware of them, what they were going to do, but we never agreed to go anywhere together."
The trio will now line up together in MLS is what will prove to be a huge coup for club president David Beckham.
Inter Miami will hope their investment can pay immediate dividends with the club languishing at the bottom of the table.
A poor start to the season saw Phil Neville axed as head coach at the start of June, allowing Martino to take the reins.
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Even with Messi and co at their disposal, their one win in ten games may prove too much of a disadvantage to make this season's play-offs, as they sit nine-points adrift of Montreal who currently occupy the final spot.