Simple answer: If your employer includes the reimbursement, as income, in box 1 of your W-2, it is taxable income to you. If he does not, then it is not taxable and you do not need to report it.
But taxes aren't simple. As others have stated, your employer must have an "accountable plan" for employee expenses. The fact that he reimburses you for actual expenses, as oppressed to giving you a "car allowance", probably meets that requirement.
if it is included on your W-2 (and hence taxable), be advised you, as a W-2 employee, are not longer allowed a mileage deduction (beginning in 2018).
