The club's recent overhaul comes as it is about to emerge from the All-Star break for a venture into the new Leagues Cup and a home match against Mexico's Cruz Azul on Friday. Messi is expected to make his Inter Miami debut in that match.
Alba, 34, played 11 seasons at Barcelona, helping the legendary Spanish club to six LaLiga titles. He also played for Valencia. The attacking left-back had 37 goals with 107 assists in 605 matches across all competitions.
"Jordi is an accomplished, dynamic and experienced player that we're excited to acquire to continue bolstering our squad," club sporting director Chris Henderson said in a release. "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."
The trio of former Barcelona players will reunite with Gerardo "Tata" Martino, who just moved into the head coach role for the last-place team in the Eastern Conference.
Inter Miami is 5-14-3 (18 points) during the MLS season and are 12 points below the playoff line with 12 regular-season games remaining.
Alba has made 93 international appearances for Spain and was part of the squad which won Euro 2012 and this year's UEFA Nations League.