The announcement of the deal, which includes a club option for 2025, came two days after Inter owner Jorge Mas said Alba was on the way.
He will join Argentine superstar Messi and Spanish midfielder Sergio Busquets (35), another former Barcelona player, as Inter, co-owned by former England great David Beckham, seek to reverse their flagging MLS fortunes.
Alba, who has made 93 appearances for Spain, terminated his contract with Barcelona in May.
The left-back won six Spanish league titles with Barça and was part of the team which won the 2015 Champions League.
He also played in the Spain team which won the 2012 European Championship.
"Jordi is an accomplished, dynamic and experienced player that we're excited to acquire to continue bolstering our squad," said Inter sporting director Chris Henderson. "He has proven for over a decade that he is one of the best fullbacks in the sport due to both his defensive solidity and capacity to contribute in the attack.
"We know that he'll help Inter Miami achieve the Club's objectives this season and beyond."
Inter said in their statement that Alba was "expected to join the team in the coming days."
Meanwhile, Messi and Busquets took part in their training session with Miami on Tuesday and are expected to make their debuts for the club - perhaps not in starting roles - on Friday against Mexico's Cruz Azul in the Leagues Cup.
