Park, one of the so-called Three Bears group of shareholders, owns more than six per cent of the club and joined the board in March.
The Lanarkshire businessman spends much of his time in Spain and his son, Graeme, will take his place on both the football and PLC boards.
A club statement read: “Mr Park feels he cannot at this time make a full contribution to the running of the club and company because of other commitments.
“The board thanks Mr Park for his valuable contribution which helped ensure boardroom change earlier this year.”
Park added: “I would like to put on record that although I held the position as director for only a short period of time it has been an honour and a privilege to serve the club and I will always be proud of the part I played in bringing this great institution back into the hands of those who have its best interests at heart.
“I am confident that going forward the club is in good hands and will offer all my support to the board in pursuing what is best for the club. Rangers is hugely important to me and my family and I am delighted that Graeme is joining the board.”
Meanwhile, the Rangers First fans’ group has announced the purchase of almost 600,000 shares.
The group has added 586,000 shares to take its total to more than 2.6 million or 3.2 per cent of the company.
Rangers First director Ricki Neill said: “The support and financial backing we’ve had from the Rangers First members has been overwhelming.
“It has allowed us to increase our holding in the club and I would urge all Rangers fans to join Rangers First and help drive us towards our first target of five per cent. You can commit from as little as £5 a month.
“We must keep this momentum going to ensure a stronger Rangers off the park. Our club is at last in good hands and moving in the right direction but to absolutely ensure we never return to dark days it is vital Rangers fans own a significant shareholding.”