Gers director Park was invited to join the club's board in 2015 by South Africa-based King after the old regime was voted out at the AGM.
The Park's Motor Group founder spent five months on the board before stepping down and being replaced by his son, Graeme, in August 2015, due to other commitments.
"Rangers International Football Club Plc ("RIFC") is pleased to announce that Douglas Park has become deputy chairman of the club," a statement read.
"Mr Park, now based in Scotland, has kindly made himself available to adopt a more prominent position within the club. The role of deputy chairman allows Douglas to assist the club by providing an important local interaction between RIFC and the executive running the football club.
"This appointment was requested by the chairman who believes that the position of a Scottish-based deputy chairman will assist him in the ongoing implementation of the club's business strategy."
The 68-year-old joined the RIFC plc's board in November 2015, and is the fifth largest shareholder with a six per cent stake.