Richard Bossons, part of the cathedral's masonry team, said the design would complement the medieval facade of the 800-year-old building.
The 6ft 7in (2m) tall statue, weighing almost two tonnes, will sit in an empty niche on the minster's west front.
It will be installed in 2022 to mark the 70th anniversary of the Queen's accession to the throne.
Mr Bossons, (see left of photo with the Dean of York Minster,Dr Jonathan Frost) said the statue had been a challenge to design.
"The statue needs to be part of the fabric, not a distraction from it, yet it also has to have the poise and presence befitting of the Queen's unique role," he said.
The statue will depict the Queen wearing Garter robes and the George IV State Diadem and holding the orb and sceptre, the symbols of her authority.
It will be carved from a block of Lepine stone, a French limestone previously used for other figurative carvings at the cathedral.
"She will stand proud and resolute in her niche, welcoming worshippers and visitors alike," Mr Bossons said.
The statue will overlook a new public square, proposed for the west front of the minster, to be called Queen Elizabeth Square.
The Dean of York, Dr Jonathan Frost, said he hoped the statue would "inspire the city and be a cause for celebration as we recover from the pandemic".
The initial design has been developed in consultation with York's Fabric Advisory Committee and the Cathedrals Fabric Commission for England, who have given permission in principle for the statue under the Care of Cathedrals Measure, which is the legal framework against which all major changes to cathedral buildings are considered.