The decision will allow workers to begin drilling as scheduled in early November.
Regulators also approved depositing the 400,000 cubic yards of dirt produced by drilling on Virginia Key. Miami-Dade County must certify the fill is clean and approve a plan to use it for the island's environmental restoration.
Some environmentalists and park activists had raised concerns about depositing fill in Virginia Key, a barrier island off Miami.
The permits will be final unless an objection is filed within 21 days.
The project will create two separate tunnels scheduled to open in 2014.