The new deal will keep Amat at the Premier League side until 2019.
“This is my home. I am happy here and my family is too,” said Amat.
“It’s great news and I’m so happy to sign a new extension.
“I’ve been here for two and a half years and I’m very happy to be here for another three years.”
The 23-year-old joined the south Wales club from Espanyol for £2.5million in the summer of 2013.