The deal is thought to be worth around £300,000 to the Claret and Blue for whom Routledge made just two substitute appearances.
The former Spurs and Crystal Palace wideman failed to break into the first team with Ashley Young and James Milner dominating the wide berths.
Routledge had been on loan at Cardiff and was expected to join the Bluebirds, who were very keen to sign him.
Chairman Peter Ridsdale said that the club had made a very generous offer to winger but he instead opted for a move to London.