Keane was heavily linked with a move for the 26-year-old frontman during the summer but Murphy remained at the Premier League club.
Murphy has been allowed to move on after making just seven first-team appearances this season.
He joins fellow former Black cats Carlos Edwards, Grant Leadbitter and Jon Steadat the Championship club.
Earlier on transfer deadline day, Ipswich allowed fellow frontman Tamas Priskin has to join QPR on loan until the end of the campaign.