The former Ibrox manager called time on the role he has held since May following the return to Ibrox of former chief executive Charles Green.
Green was appointed in an advisory capacity last Friday prompting rumours that Smith would consider his future at the troubled club.
In a statement to the Stock Exchange, the club said: "Rangers announces that Walter Smith has today resigned from his position as Chairman and a director of the Company with immediate effect."
Green appointed Smith to the board last November after buying the assets and business of the liquidation-bound club five months previously.
At the time the move was seen as a coup for Green, who stood down from his role as chief executive in April amid an investigation into his links with former Rangers owner Craig Whyte.
The following month, Smith was elevated to his position following the departure of former chairman Malcolm Murray.
Smith's departure is likely to spark a bitter power-struggle for the League One side with manager Ally McCoist, who came under fire from Green last Saturday, now likely to consider his future.
Green claimed McCoist's side would have to win more than the league title for the season to be a success prompting a brutal backlash from the Ibrox legend.
After seeing his team crash out of the Scottish League cup at the first hurdle at the hands of Forfar, McCoist said: "He is an embarrassment. I was appalled by his comments.
"If that was a threat, the self-proclaimed straight-talking Yorkshireman should know that boys from the West of Scotland don't scare easily."