You are not required to pay taxes on the amount if your employer directly pays your moving expenses.  However, you might still be required to file a Form 3903 for moving expenses, depending on how the amount is reported on your W-2.  

In most cases, you can consider moving expenses incurred within 1 year from the date you first reported to work at the new location as closely related in time to the start of work.  After a year, you will no longer meet the time test for moving expenses.