The windows date back to 1404 and tell the story of the spread of Christianity across the north of England.
Work to replace the medieval glass is expected to take 11 years to complete, according to the cathedral.
It is part of a 20-year project with the cathedral and York Glaziers Trust to add environmental protective glazing to more than 70 of its unprotected windows, buying time for other conservative work.
The restoration will also include maintenance of stones in the Cathedral's South Quire Aisle, which dates from the late 1300s.
The project is supported by an innovative fundraising campaign organised by the York Minster Fund and the Heritage Lottery Fund.
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