The club confirmed the move in a statement to the Stock Exchange, a move that comes at the end of weeks of in-fighting at the club and numerous attempts to remove Murray.
The club held a board meeting in London on Wednesday in an effort to put an end to the turmoil, and after Murray agreed to step down Smith's appointment was unanimously approved by the board.
Smith, who won 10 league titles while manager at Ibrox, has been a non-executive director since last November.
"Rangers should always be at the pinnacle of the game and the fans deserve nothing less," Smith said.
"Although I have been on the board for some months this will be another departure for me but there are enough directors around to make sure we will make the kind of progress necessary and which our fans want.
"Unity among the directors is vital. We must all be on the same page as often as possible. We won't always agree but Rangers, this club and our fans must always come first.
"It is a great honour to be asked to take up this position and it goes without saying that I feel proud as well as humble. However, no one should believe that I see my role as a passive one.
"That hasn't been my way in the past and it won't be my way in the future."