Jordi Alba has 93 caps for Spain, captaining the side that won the Nations League in June
The Spain full-back, 34, has signed a contract to the end of the 2024 Major League Soccer season, with a club option for 2025.
Alba left Barca this summer after 11 years with the Spanish giants.
"We know that he'll help Inter Miami achieve the club's objectives this season and beyond," said Inter Miami's sporting director Chris Henderson.
Alba helped Barca win six La Liga titles and the Champions League in 2015 while winning Euro 2012 and the 2023 Nations League with Spain.
Argentina World Cup winner Messi, 36, and Alba's fellow Spainiard Busquets, 35, have already made the switch to the United States' Major League Soccer.
Messi and Busquets, who have signed deals until 2025, were presented to a cheering crowd of around 20,000 Inter Miami fans at the club's DRV PNK Stadium on Sunday, flanked by co-owner and ex-England captain David Beckham.
Seven-time Ballon d'Or winner Messi trained with his Miami team-mates for the first time on Tuesday and is expected to make his debut in their Leagues Cup opener against Cruz Azul, of Mexico City, on Friday (01:00 BST, Saturday).
Alba, who played 459 matches for Barca and has 93 Spain caps, should be available to face Atlanta United on Tuesday (00:30 BST, Wednesday).
"Jordi is an accomplished, dynamic and experienced player that we're excited to acquire to continue bolstering our squad," Henderson added.
"He has proven for over a decade that he is one of the best full-backs in the sport due to both his defensive solidity and capacity to contribute in the attack."
Alba had another year remaining on his contract with Barca, who he joined from Valencia in 2012, but they agreed to release him in May.
Meanwhile, US reports have linked Inter Miami with another former Barcelona player - 36-year-old Uruguay striker Luis Suarez, who is currently playing for Brazil side Gremio.
The ex-Liverpool forward played alongside Messi, Busquets and Alba during six seasons at the Nou Camp between 2014 and 2020.
Inter Miami's club president Jorge Mas said on Tuesday: "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."
-- Courtesy of BBC Sport