Scotland's Transport Minister Keith Brown said it was a welcome announcement for both passengers and the air industry.
He said: "We look forward to a long and productive relationship with Virgin Atlantic and the exciting connections they can offer with all the benefits that will bring for passengers, Scotland's aviation industry and the wider Scottish economy.
"The detail will be worked out over the next couple of weeks but we are pleased that the European Commission has taken note of the need for both Edinburgh and Aberdeen to be served and that Virgin Atlantic will now be able to operate from two of Scotland's most important cities."
The minister said he remained concerned about the lack of competition on the Glasgow to Heathrow service as a consequence of Bmi's withdrawal of the service last year.
Glasgow was not part of the remedies package considered by the European Commission.
- Virgin plans to begin services on March 31 2013 and will primarily focus on multiple daily flights between Heathrow and Edinburgh and Aberdeen.
- The new routes, on which Virgin will compete with long-time rival British Airways, will complement the new Heathrow-Manchester route the airline is also introducing next year.
Sir Richard Branson's airline Virgin Atlantic is poised to begin new domestic services from Heathrow Airport starting from March 2013.
Virgin said today it had been offered short-haul take-off and landing slots available following the takeover of bmi by British Airways's parent company IAG.
Virgin Atlantic has called on the Government to make a decision on airport capacity after Number 10 insisted there was no third runway to be built at Heathrow.
The Virgin Atlantic plane that was forced to make an emergency landing at Gatwick Airport last week has been examined and has been certified for a return to service.
A spokesman for Virgin Atlantic said: "The investigation identified that a number of alarms were triggered in flight, in response to which our flight crew took positive action in line with procedures by returning to Gatwick and completing an evacuation of the aircraft.
“The flight crew and cabin crew followed safety procedures at all times and carried out their duties in a professional manner to ensure the safety of our passengers was maintained throughout the flight and during the evacuation."
Privacy lawyer Gerald Shamash has told the Guardian that the allegations a Virgin Atlantic employee passed on information about eight celebrities is "extremely worrying" and "this could be the tip of the iceberg".
Mr Shamash also said advance knowledge of the whereabouts of celebrities was the "bread and butter" of life as a picture agency or tabloid newspaper.
Reacting to the allegations that an employee at Virgin Atlantic passed the flight details of eight celebrities including the footballer Jermaine Defoe to a paparazzi agency, a spokeswoman for the footballer said:
"This is a serious breach of privacy. We'll be consulting with our lawyers and investigating the matter further."
Virgin Atlantic sources told The Guardian that four of the eight celebrities whose flight details were allegedly leaked to a paparazzi firm, flew on the dates given by the airline employee.
Ashley Cole and Sienna Miller were pictured in Heathrow and Los Angeles respectively, on the dates allegedly provided. The other four celebrities are believed to have cancelled their flights.