Tate is currently sidelined after breaking his leg in a golf buggy accident 10 days' ago, and is expected to be out of action for up to six months.
The 28-year-old joined the Swans from Manchester United on loan during the 2002-03 campaign, before joining permanently in 2004.
He has since gone on to make over 300 appearances for the club and was glad to secure his future in south Wales, despite his injury absence.
He told the club website: "I'm delighted to sign the contract because is shows the club have a lot of faith in me.
"It will take me well into my 30s and who knows what will happen beyond that, although obviously I would like to stay even longer.
"It will depend on injuries and form, but I would love to finish my career at Swansea and, with a bit of luck, I hope that could happen.
"We've been talking about a contract for a while. The injury delayed things a bit. I was meant to sign before I got injured, but then it got put on the backburner.
"Then it was deadline day, which held things up again, but the new contract was never under threat because of the injury.
"The club could see it was an unfortunate accident which no-one could have expected."
Tate is the latest in a long line of Swansea players to commit their futures to the Premier League newboys with Neil Taylor, Garry Monk, Joe Allen, Angel Rangel, Nathan Dyer, Ashley Williams and Andrea Orlandi among those to pen new deals.