A week of negotiations between the upper and lower houses of the parliament has resulted in both chambers passing the agreement, with proposals that a nationwide referendum be held on the matter being dropped.
It now means that the Swiss Federal Tax Administration (STFA) can pass on the details of 4,450 UBS account holders suspected of evading tax in the US ahead of an August 19th deadline.
The STFA said that the decision means 1,200 cases are ready to be disclosed to American regulators immediately.
It explained that a total of 3,000 files have been processed so far, with around 40 people employed on the task.
"Almost all of the remaining cases - roughly 1,450 - are already being processed, so efforts to comply with the treaty assistance request are on course," it was explained.
In February of last year, UBS agreed to a $780 million settlement to end criminal charges made against it in regard to allegations that it was aiding its American clients in tax evasion practices.
The deal to hand over the data was agreed by UBS back in August 2009 in order to bring an end to a follow-up civil action lawsuit brought against it by US authorities.
Inland Revenue Service commissioner Doug Shulman welcomed the news of the parliamentary vote.
"We will immediately follow up on the information we receive from the Swiss," he stated.
The decision has also been praised by UBS, which labelled the vote an "important step".
"UBS continues to focus on its comprehensive and timely compliance with all obligations â¦ and is confident that this will be achieved by the relevant deadlines in August 2010," the Swiss bank said.
By Claire Archer