Cardiff will allow long-serving Kevin McNaughton to leave this summer along with Danny Gabbidon and Nicky Maynard.
Highly-rated Atletico Madrid midfielder Saul Niguez has signed a new five-year contract.
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."