Messi announced last month that he will be joining the side co-owned by David Beckham following his departure from Paris Saint Germain.
The 36-year-old seven-time Ballon D'or winner could make his debut for Inter Miami against Cruz Azul in the Leagues Cup on Friday.
The World Cup winner said in a statement from the club: “I’m very excited to start this next step in my career with Inter Miami and in the United States.
“This is a fantastic opportunity and together we will continue to build this beautiful project. The idea is to work together to achieve the objectives we set, and I’m very eager to start helping here in my new home.”
Beckham added: “Ten years ago, when I started my journey to build a new team in Miami, I said that I dreamt of bringing the greatest players in the world to this amazing city.
“Players who shared the ambition I had when I joined LA Galaxy to help grow football in the USA and to build a legacy for the next generation in this sport that we love so much.
“Today that dream came true. I couldn’t be prouder that a player of Leo’s calibre is joining our club, but I am also delighted to welcome a good friend, an amazing person and his beautiful family to join our Inter Miami community.
“The next phase of our adventure starts here, and I can’t wait to see Leo take to the pitch.”
MLS commissioner Don Garber said: “We are overjoyed that the greatest player in the world chose Inter Miami CF and Major League Soccer, and his decision is a testament to the momentum and energy behind our League and our sport in North America.
“We have no doubt that Lionel will show the world that MLS can be a league of choice for the best players in the game. We look forward to seeing his debut for Inter Miami in our Leagues Cup tournament later this month.”