Rangel has spent 11 years with the Swans, playing 373 times after joining from Spanish semi-pro side Terrassa for a fee of just £10,000 back in 2007.
The right-back, described in the statement as the "best the club has ever had", was part of the side that won two promotions to get Swansea to the Premier League.
However, he has featured just six games this season and now feels it is the perfect time to move on.
“I know this season has been difficult for me,” the 35-year-old said. “I haven’t had many games so it is difficult for the club to give me another extension, I understand that.
“I will look somewhere else for one or two more seasons. When I am 37 or 38 it will be time to call it a day and hopefully I will come back and help the Swans in another way. Until then, I will always be looking at Swansea’s results.
“This is my club. I have been lucky enough to be a player for Swansea and now I will be a fan.
“I will always want the club to do well. Hopefully, when I finish playing, I will be a season-ticket holder at the Liberty and I will be able to watch a successful team because I am a Jack.”
10 May 2018