The sale to Stonepeak Partners requires City Council approval.
But a vote over the original deal was delayed due to pushback from city aldermen who criticized the process.
The new proposal includes a $75 million payment to the city plus a sharing of profits on an annual basis.
Stonepeak also agreed to sell off its stake in a company that provides deportation flights for the Department of Homeland Security.
Mayor Richard M. Daley first sold off the rights to the city's parking meters for more than a billion dollars in 2008.
It's believed the return on that sale has doubled in the years since.