The House approved the negotiation framework by a vote of 426 to 20.
The FATCA was enacted in 2010 by Congress to target non-compliance by US taxpayers using foreign accounts.
Aimed at tackling tax evasion, the Act requires foreign financial institutions to report to the Internal Revenue Service information about financial accounts held by US taxpayers, or by foreign entities in which US taxpayers hold a substantial ownership interest.
The US has so far struck intergovernmental agreements with Denmark, Germany, Ireland, Mexico, Norway, Spain, the United Kingdom and Japan.
Deputy Prime Minister and Finance Minister Kittiratt Na-Ranong said the law would be executed only on US taxpayers, and the negotiations followed the conclusion by Thai financial institutions that there should be a government-to-government agreement on the matter.
Parliamentary approval would be sought if Thailand needed to revise any law pursuant to the talks, he added.
Democrat MP Kiat Sittheeamorn raised concerns over legal amendments in the future.
With China had not yet having signed an intergovernmental agreement, Thai officials must be able to explain how Thailand would benefit from this agreement. Alternatively, they should ask if it is possible for the US to strike an agreement with Asean as a whole, he said.
Democrat MP Alongkorn Ponlaboot said that under the FATCA, financial institutions in foreign jurisdictions would work as if they were units under the US Revenue Department.