Virgin Atlantic President, Sir Richard said: "This is an exciting day in Virgin Atlantic history. It signals the start of a new era of expansion, financial growth and many opportunities for our customers and our business.
"I truly look forward to the possibilities our partnership with Delta will offer. We have always been known for our innovation and service and have punched above our weight for 28 years.
"That is why our customers love us so much. We will retain that independent spirit but move forward in a strengthened partnership with Delta.”
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.