Access shuttles the disabled through their daily errands, employing about 62 drivers.
The contract replaces current operator, MV Transportation. MV entered a bid of about $33 million for the seven-year contract.
The vote was originally scheduled to be taken by the RTC board on April 16. However, prolonged discussion and possible legal issues delayed the vote until Friday.
According to testimony from First Transportation officials, the current Access drivers will be retained under the new contract. Many Access riders at the April 16 meeting voiced their concern to the board that their trusted drivers would be fired and replaced with those selected by First Transportation.