Yes, report relocation assistance money on your tax return (it is taxable). You may receive a 1099-MISC form for this payment. Either way, enter the income received as Other Income on line 21 of your 1040.
In TurbTax under Income and expenses, select Miscellaneous Income, then Other Reportable Income. Type in the description and amount. Item will then flow to line 21 on your 1040.
You can enter the information from your 1099-MISC for relocation assistance in the federal section of the program.
You will not be able to offset your relocation expenses as this deduction was removed as a tax deduction with the Tax Reform Act.