Since you were an employee then that amount should already be reflected in box 1 of the W-2 so you are only taxed once. Ask your employer for clarification.
However, the qualifying moving expenses can be claimed as an adjustment to your AGI.
https://ttlc.intuit.com/questions/1901337-form-3903-moving-expensesMoving expenses are limited to -
the cost of transportation of your household goods and family effects,
travel costs (including lodging but not meals) of you, your spouse and your dependents while en route
the cost of storing and insuring household goods and personal effects within any period of 30 consecutive days after the day your things are moved from your former home and before they are delivered to your new home. (Different storage rules apply to a foreign move.)
You cannot deduct the following items as moving expenses.
• Any part of the purchase price of your new home.
• Car tags.
• Driver's license.
• Expenses of buying or selling a home (including closing costs, mortgage fees, and points).
• Expenses of entering into or breaking a lease.
• Home improvements to help sell your home.
• Loss on the sale of your home.
• Losses from disposing of memberships in clubs.
• Mortgage penalties.
• Pre-move house hunting expenses.
• Real estate taxes.
• Refitting of carpet and draperies.
• Return trips to your former residence.
• Security deposits (including any given up due to the move).
• Storage charges except those incurred in transit and for foreign moves. "In transit" includes any 30 day period including the day of the move.
• Temporary lodging at the new residence location
See IRS Publication 521 on moving expenses here:
http://www.irs.gov/publications/p521/ar02.html#en_US_publink100043359