The full back was due to be out of contract in just a matter of days, but has now agreed to a new three year deal at the club which will be signed in the next few weeks.
Rangel was an ever-present in the team which gained Premier League promotion and has made 159 appearances for Swansea since making the move from Terrassa in the summer of 2007.
"We are very happy to secure Angel's future for the next three years," chairman Huw Jenkins told the official site.
"He has played a big role in the club's success since he arrived here, and we were very keen for him to be part of our plans going into the Premier League.
"Over the last few years there has been interest from Premier League clubs in Angel, but he is very pleased to have achieved his dream of reaching the Premier League with the club he left his native Spain for."