The image shows two pairs of baby feet and was accompanied by a captioned that revealed the boys' names.
"They're home!! Tristan and Sasha came into the world on March 18 right after the full moon. Complete happiness," Pataky wrote.
Pataky gave birth to the twins at the Cedars Sinai Medical Center in West Hollywood, Calif. on Thursday night.
The Thor star and the Spanish beauty married in 2010. The couple welcomed their first child, a daughter named India Rose, in May 2012.