Heathrow Airport Holdings, the parent company for both airports as well as Heathrow, announced yesterday that it was putting them on the market. It hopes to complete sales before the end of the year.
It is also putting Southampton Airport up for sale. The move did not come as a surprise after months of rumoured bids.
Spanish firm Ferrovial was reported to have made an £800 million offer to buy the airports in February. The company already has a 25 per cent stake in HAH, previously known as BAA.
A consortium led by Zurich Airport and the investment firm Partners Group, is also believed to have had an offer rejected.
A spokesman for Heathrow Airport Holdings said: "Over recent months Heathrow Airport Holdings group shareholders and management have been considering their strategic position in relation to our three airports, Aberdeen, Glasgow and Southampton.
"As a result the group is now formally entering a sale process."
Potential bidders could include Global Infrastructure Partners, the group which bought Edinburgh Airport from BAA in 2012. Others include Manchester Airport Group, which owns Manchester Airport and London Stansted or an overseas pension fund.
Glasgow Airport is the second busiest in Scotland but its passenger figures have yet to recover to pre-credit crunch levels. It has just completed a £17m overhaul of its terminal, which Managing Director Amanda McMillan described as "one of the most significant and comprehensive upgrades" since the airport was opened in 1966.
Aberdeen is a key base for the offshore industry and passenger traffic returned to 3.4 million last year, matching 2007 levels.
Aviation industry consultant Douglas McNeill said neither was an "unmissable opportunity" for investors, but each would benefit from being free of HAH.
He said: "Heathrow is enormous, so it inevitably gets the lion's share of management attention in the current structure. It would be good for both Glasgow and Aberdeen to achieve a little independence.
"Aberdeen is particularly prosperous as it's very much geared to the oil and gas industry. With Glasgow, the catchment area is less prosperous but much bigger. As far as a quick sale goes, it depends how hard a line [HAH] want to drive on price, but they'll have an idea what they're after. Whoever buys them the airports are likely to get more investment than they have under [HAH]. That's been the experience at Gatwick and Edinburgh, up to a point, so that's a reasonable expectation."
Gareth Williams, director of policy at the Scottish Council for Development and Industry, said: "Both airports are major gateways and important employers for their city-regions and the country, and they work closely with the public and private sectors to promote their areas globally, support major events and develop services which will benefit key industries.
"Building on the success of the Commonwealth Games and of the oil and gas industry domestically and internationally, it will be vital to ensure that these strong relationships, investment in improving infrastructure and facilities, and efforts to attract new international routes continue under new ownership."
l An investigation is under way after a collision between two vehicles at Edinburgh Airport which closed the runway for 20 minutes.