“In Diego we found a manager that fits our culture and has a strong desire to build a winning club for our fans,” said Inter Miami spokesman Paul McDonough.
“He brings a lot of experience and championship-winning mentality as we begin our drive to be among the best clubs in the Americas.
“We have big aspirations for our club and believe Diego has the right drive, passion and leadership to accomplish our goals.”
Inter Miami, which opens the season March 1 against Los Angeles FC, is owned by five people, including Beckham.
Alonso, the only coach to win the CONCACAF Champions League with two different teams, reportedly beat out former New York City manager Patrick Vieira and former DC United midfielder Marcelo Gallardo for the job.
The 44-year-old Alonso most recently served as head coach for Monterrey in Mexico.
He was fired three months ago after a 2-0 loss to rival Tigres.
Before being sacked he led Monterrey to the 2019 CONCACAF Champions League title.
Two years earlier he guided Pachuca to the CONCACAF Champions League crown.