Chelsea full-back Cesar Azpilicueta has been handed a new five-year deal by the Premier League leaders.
Scottish FA confirms it will apply to FIFA for an exception to help push through John Guidetti's loan move to Celtic.
Rangers said Traynor, who left his role with the Daily Record on Sunday and has ceased working as a BBC Radio Scotland presenter, would oversee the development of all of the club's media platforms from early next year.
A statement read: "James joins Rangers following a distinguished journalistic career with The Herald, Express and Daily Record newspapers as well as being a presenter with the BBC.
"In his role at Ibrox, James will be supported by the Rangers Media editorial team, the press office and external media advisers, Media House."