The new 18,000-seater stadium will be built on the site of Lockhart Stadium, former home of the Fort Lauderdale Strikers and defunct MLS team Miami Fusion, which has fallen into disrepair.
Inter Miami will join MLS next season but currently do not have a stadium.
The club are hoping to complete negotiations to build a stadium in Miami, near the airport, in order to move back to the city when the proposed "Miami Freedom Park" is completed.
Former Manchester United and Real Madrid midfielder Beckham and his team of investors will also base their youth academy at the site in Broward County, which neighbours the city of Miami.
Inter Miami also intend to have their administrative centre and an affiliated second division team at the venue.
"We have made a proposal...about revitalising and activitating this site, what was a historic stadium which was always the home of professional soccer in South Florida with a lot of history," said businessman Jorge Mas, Beckham's partner in the club.
"This is a great opportunity to create new memories for this site – our academy and training centre will be based here but also we will activate this site with an 18,000 brand new stadium, it will be ready to host our first two seasons of MLS here," Mas said.
Beckham said although the team still intended to have their main stadium in Miami, the Lockhart venue helped the club appeal to a wider community.
"We will be in Miami but our commitment is also to South Florida. We are not coming here for just for two years and then abandon this - this is a long-term project," he said.
The proposals will need to be backed by the city of Fort Lauderdale at a meeting on Tuesday where a rival bid will also be presented.
FXE Futbol intend to create a venue for a projected United Soccer Leagues (second tier) team and family sports facilities.
(Reporting by Simon Evans, editing by Ed Osmond)
