This calendar year 2018, you can deduct moving expenses only if you are an active duty member of the Armed Forces and meet certain other requirements such as a military-ordered permanent change of station (PCS).
But what if your moving expenses were paid out of pocket in 2017, and your move also occurred in 2017, and you were not reimbursed until this year, 2018? The IRS just issued some guidance on this very situation in their Notice 2018-75 which states that if your employer waited until 2018 to reimburse you for those expenses, then the reimbursements should be excluded from your wages on the W-2 and are also not subject to federal income taxes or the payroll taxes.
Be careful! If you already took a deduction for those expenses in 2017, then there will be some reconciling to do on your part. You cannot take the deduction for them in 2017 and then have the reimbursement free from tax!
If you moved in 2017 and your employer reimbursements were late in coming to you, be sure you check your W-2 carefully when it arrives in January or February 2019. Call your employer's HR or payroll department to verify all the items on it. If you are unsure how to treat any out-of-pocket expenses and/or reimbursements, call a tax advisor for assistance.