The Premier League new boys completeda move for Leroy Lita on Wednesday and Routledge has followed suit for an undisclosed fee after completing his medical.
Wayne's world: Routledge has completed move from Newcastle to Swansea
The 26-year-old former England Under-21 international has put pen to paper on a three-year contract and will compete with Scott Sinclair and Nathan Dyer for a wing spot at the Liberty Stadium.
Routledge told the club website: 'I'm looking forward to the challenge.
'It's taken a couple of days to get everything agreed, but I'm excited about getting started.'
Rodgers and in: Routledge was impressed by Swansea manager
Routledge has plenty of top-flight experience having had spells at Tottenham, Portsmouth, Fulham, Aston Villa and Newcastle.
He impressed during his loan spell at QPR last season, and was a key figure in helping the London club to the Championship title.
And Routledge says he is eager to work with Swans' manager Brendan Rodgers having admired the south Wales' club's attractive style of play.
'I've had a good chat with the manager and he really impressed me,' he said.
'I had heard a lot of good things about him and the chat only reinforced my belief that moving to Swansea was the right thing to do.
'Having watched Swansea last season, I think everyone would agree they were the best footballing side in the Championship.
'It's going to be a difficult first season in the Premier League; it's going to be tough. But everyone is confident and looking forward to it. After all, playing in the Premier League is what you dream of.
'I'm excited about it.'
Rodgers is still hoping to add two goalkeepers to his squad before the transfer window closes.
Trialist Gerhard Tremmel turned in a composed display in Wednesday's 2-0 friendly win over Celtic and may yet join the club on a full-time basis.
Swansea are also interested in bringing in Nottingham Forest keeper Lee Camp, but have so far seen their bids rebuffed by the east Midlands club.
Trialist Tremmel could be the answer to Swansea's keeper headache, says RodgersSwansea 2 Celtic 0: Cervi drops a clanger and Loovens suffers injury blowAll the latest Swansea news, features and opinion