The new 180 million complex at Prestwick in Ayrshire replaces a 30-year-old adjacent building and also takes over from a control centre in Manchester.
The scheme, which has been in the pipeline for a decade, is also expected to provide a significant economic boost to the west of Scotland economy.
The centre's 900 staff include 130 air traffic controllers who have transferred from Manchester, each of whom earns up to 91,000 a year.
Manchester controllers handed over control of their airspace at 3am on Saturday, ending 35 years of operations there.
The three separate parts of the Prestwick complex collectively control more air space than any other European control centre.
The Scottish area control centre will control nearly one million flights a year – 42 per cent of the 2.2 million using UK airspace under air traffic control, and up from one third previously. UK flights carry a total of more than 200 million passengers.
Prestwick's oceanic area control centre controls nearly 400,000 flights over the eastern half of the north Atlantic, from the Azores to near Iceland.
The new building also houses an RAF air traffic control centre, responsible for military aircraft flying over Scotland and northern England, and all aircraft emergencies.
Nats, the former part-privatised National Air Traffic Services which runs the centre, said the project had been completed on time and under budget.
However, it was put on hold for two years after the terrorist attacks on aircraft in the United States on 11 September, 2001, which led to a temporary decline in transatlantic flights.
The scheme completes the halving of UK air traffic control centres, following the closure of the West Drayton centre near Heathrow three years ago. The other remaining centre is at Swanwick, near Southampton.
Transport secretary Lord Adonis said: "This new, state-of-the-art centre forms part of the ongoing modernisation of our air traffic control services, and will help Nats to manage UK aviation in a way which is both greener and more efficient."
The Prospect union, which had expressed fears about the development of the new centre, said these had been put to rest. Garry Graham, its national secretary for aviation, said: "It appears everything has gone smoothly, which is a tribute to the hard work of air traffic controllers and engineers. Any concerns we had have been allayed."
The centre will be officially opened by the Princess Royal on 5 February.