Rangel put pen to paper on fresh terms at the Liberty Stadium on Tuesday, and the Welsh club have now tied down Amat for a further year, with the 22-year-old's original deal due to expire in 2017.
Amat is in his second season with Swansea, having joined from Espanyol in June 2013.
"I'm so happy because it's important to know the club has confidence and faith in me," Amat told Swansea's official website.
"I work hard every day for this and the chairman has been very good to me, so I was delighted to sign an extension.
"I'm very happy to be here. It's a very exciting time to be part of this club. The team, the staff, the club - it's a big family here and I really like that.
"It was a big decision to move my family here. I was moving to a new country and a new league, but it has worked out really well and we really enjoy our time in the city and talking to supporters.
"I've played games in the Premier League, the cups and the Europa League, so it has been an amazing experience for me here already.
"But this is hopefully just the start. It's getting better every year at the club, we are achieving more and more."
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