Martino will come in as a replacement for Phil Neville, who was sacked at the start of this month, with Miami bottom of Major League Soccer’s Eastern Conference zone.
The 60-year-old was without a club after leaving Mexico following their group stage elimination at the 2022 FIFA World Cup in Qatar.
Messi will join Inter Miami as a free agent next month after his Paris Saint Germain contract expires. He will also be followed by former Barcelona teammate Sergio Busquets.
Martino previously coached Messi at Barcelona in the 2013/2014 season and again at the Argentina national team between 2014 and 2016.
Martino said in a club statement: “I’m very excited to join a big club like Inter Miami and I know together we can accomplish many great things.
“The club has the necessary infrastructure to be a major competitor in the region and I believe that with everyone’s hard work and commitment we can get there.”
Inter Miami co-owner David Beckham added: “’Tata’ is a highly respected figure in our sport whose track record speaks for itself.
“We are confident that his achievements in the game and experience as a head coach will inspire our team and excite our fans and look forward to seeing the impact he will have on and off the field.”
In his previous stint as a manager in the MLS, Martino led Atlanta United to MLS Cup glory in 2018.