Weighing 1.1 tonnes and made from French limestone, it shows the Queen in the robes of the Order of the Garter.
Richard Bossons, 52, who has worked at the minster for 11 years, won a competition to create the statue, which stands above the West Front entrance.
It was intended to celebrate the Queen’s platinum jubilee and was completed in August, the month before she died.
He said: “I hope everybody likes it. It is the best I could pull out of myself. Hopefully, I have done justice to the Queen and the King likes it and I have done justice to the front of the building.”
Mr. Bossons, who has done caricatures or grotesques for cathedral gargoyles before, said there were some nerve-wracking moments during the sculpting, which involved a three-tonne piece of Lepine limestone being cut by machines to his design and six months’ work with his chisel to refine the stone.
He said: “I am hugely relieved, and it will be nice now to go back to my bread-and-butter work.”
The design was created to give a sense of potential movement, with the Queen looking down the main approach to the minster and her left hand pulling in her robe to brace against the winds which frequently buffet the west front.
York will also get its first new public square in 200 years with the development of the area in front of the statue, which will be named in the Queen’s honor.
Before unveiling the statue, which is raised above street level, Charles said: “The late Queen was always vigilant for the welfare of her people during her life.”
He said her “image will watch over what will become Queen Elizabeth Square for centuries to come”.
Earlier, Charles and his wife Camilla, the Queen Consort, joined the Archbishop of York and other dignitaries for a service at the minster and looked at a new exhibition explaining how the statue was made.
They saw a scaled model of the final sculpture as well as a maquette used in the design process.
The Queen visited the minster to distribute Maundy money in 1972 and 2012.