Virgin Atlantic has been offered the rights to operate Heathrow links to Edinburgh and Aberdeen.
Sir Richard Branson's airline bid successfully for the London landing slots formerly operated by BMI.
The slots were released to others by regulators as a condition of allowing the takeover earlier this year of BMI by British Airways' owner IAG.
Virgin Atlantic intends to start operating the new services from the end of next March.
BA already flew between Heathrow and Scotland in competition with BMI, and the European Commission ruled that the London airport's scarce and valuable slots had to be released to other airlines for links to Edinburgh and Aberdeen, as well as Cairo and Moscow, where BMI and BA had formerly competed.
Virgin Atlantic is to lease Airbus A320s from another operator on its new routes.
Its first move into short-haul flights began last August, when it announced a new route between Manchester and Heathrow, building on an often bitter, 28-year rivalry between British Airways and Virgin Atlantic.
The only other airline known to have put in a bid for the slots was Aer Lingus.
Steve Ridgeway, chief executive of Virgin Atlantic, said: "We have fought hard for the right to fly short-haul and take a strong challenge to British Airways within these shores.
"This is the beginning of an exciting new era in Virgin Atlantic history and we now feel a responsibility to everyone that has supported us in this challenge."
The airline is to finalise its timetable plans over the next two weeks.
Edinburgh Airport chief executive Gordon Dewar said the new regular service would provide choice for travelling to Heathrow and open up a new set of onward destinations for passengers.
Scotland's Transport Minister Keith Brown said it was a welcome announcement for both passengers and the air industry.
Mr Brown added: "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."