Tony Pulis is disappointed by his Stoke exit but accepts chairman Peter Coates' decision.
A new fund-raising campaign called 'BuyThePars' has been launched in a bid to buy Dunfermline Athletic.
The Dutchman, who made just 13 appearance in an injury-hampered last season, was out of contract next month.
But Rodgers had made clear his intentions to keep the former AZ Alkmaar player at the Liberty Stadium.
"I've already started working towards next season, I want to return fit and fresh," Agustien said.
"I'm delighted to sign the new deal because it's a great time to be part of Swansea City and I want to help the club go higher and higher.
"The team has done extremely well this season, but we will only get better and I want to be a part of that."
Swansea have also added former Burnley and Sheffield Wednesday chief scout Tim Henderson to the club's recruitment set-up.