The creation stands 5ft 6in (1.7m) high, is 12ft 6in (3.84m) long and 5ft (1.53m) wide.
It was built following donations by visitors, who paid one pound for each brick.
The model raised 10.9 million pounds as funds for a new permanent exhibition of cathedral artefacts called Open Treasure, which is expected to attract 120,000 people a year.
Work started on the replica on 11 July 2013, which tells the story of Durham Cathedral and its place in the development of Christianity in the North East.
Durham Cathedral is a Christian Church of the Anglican Communion and the seat of the Bishop of Durham.
Durham Cathedral is one of the great buildings of Europe. Over 700,000 people visit the Cathedral every year to worship, create, explore and celebrate in the historic place.
Durham Cathedral's head of development, Gaye Kirby, said: "We've been overwhelmed by the generosity of our visitors and it has been wonderful to watch the model taking shape.
The present cathedral was designed and built under William of St. Carilef who was appointed as the first prince- bishop by William the Conqueror in 1080.
