The aim of the government is to have the bridges completed by 2021.
The group chosen will be responsible for resuming works on the project, which remain halted after the company originally selected decided to request a contract termination.
The project was presented to potential investors in Madrid by the country's vice president. Representatives from Europe and China have shown interest, according to an official.
The program is expected to benefit 6.4mn residents in the eastern zone of Mexico City, where the new international airport is being built, and Mexico state.
The public works minister said the new mechanism will shorten permitting times, allowing projects to start construction faster.