The 28-year-old Spaniard was out of contract at the end of the month and there had been fears the full-back would follow Darren Pratley and Dorus de Vries out of the south Wales club on a free transfer.
But Swans chairman Huw Jenkins told the club website: "We are very happy to secure Angel's future for the next three years. 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."
Jenkins added: "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."
Rangel will put pen to paper on his new deal within the next few weeks having previously been linked with moves to Blackpool and Fulham.
He was signed by Roberto Martinez from Spanish side Terrassa in 2007 and has gone on to become a cult hero among Swansea supporters, racking up 159 league appearances and helping the club secure the League One title and last season's Championship play-off success.
The news of Rangel's new deal is a major boost to manager Brendan Rodgers, after losing midfielder Pratley and goalkeeper De Vries, who has joined Wolves. Rodgers will now look to strengthen his squad following the news that an agreement has been reached with Ipswich over the loan of striker Tamas Priskin last term.
Rodgers, who has already signed striker Danny Graham from Watford for a club record fee of £3.5million, is set to step up his efforts to recruit reported target Grzegorz Sandomierski, with a spokesman at the Poland goalkeeper's club, Jagiellonii Bialystok, claiming Swansea were keen on the 21-year-old.
But a deal to bring Villarreal midfielder Marcos Senna to south Wales now seems unlikely due to the Spain international's wage demands.
One man who may yet leave Swansea is Wales full-back Neil Taylor. Newcastle are keen on signing the Wales defender, and had a £1million bid rejected earlier this week.
Source: PA
Source: PA