A version of the bill already passed the House last month but lawmakers will have to vote again to approve the bill as amended. House members are expected to support the amendment and the legislation could be headed for President Obama's desk as early as next week.
The White House issued a statement of administration policy on Thursday supporting both the repeal and the amendment.
The widely unpopular withholding tax was originally approved in 2006 to increase tax revenue and was scheduled to go into effect in 2013. Lawmakers repeatedly delayed the implementation debate but the Senate vote all but ensures the tax will be entirely eliminated.