With manager Roberto Martinez currently the subject of a bid from Celtic, it remains to be seen who Dyer will be playing under next season, but he is confident the Swans can flourish regardless.
"I want to be playing Premiership football and I want to get there with Swansea," he told the club's official website.
"We just missed out on the play-offs last time around, which was unfortunate. But I think we can go that one step further next season and finish in a higher position.
"I'm really happy that it's all signed and down on paper and I can't wait to get going in pre-season. From the moment I first moved here I felt it would have been the right move for me in order for me to progress with my career and develop as a player, especially with the way Swansea play football."
The money is expected to allow Southampton to continue to trade while a takeover of the club by the Pinnacle Consortium is agreed.