Flight attendants hear news of the bankruptcy
Sabena is the first European national airline to go bust in what employment minister Laurette Onkelinx has called "an economic and social disaster for Belgium".
The airline's board was finally forced to accept that its desperate search for fresh investment of 372m euros had failed on Tuesday, according to chairman Fred Chaffart.
The airline's problems started after its part-owner Swissair, which has also collapsed, reneged on a promised 136m-euro injection into the Belgian airline.
Grounded
Sabena cancelled most of its flights on Tuesday after ground staff in Brussels staged a walk-out in protest over rumours of the bankruptcy decision.
Airline staff at head-office received an e-mail telling them to collect their belongings and go home.
But the search for a rescue plan had continued until the last minute.
The Belgian government is Sabena's majority shareholder, holding a 50.5% stake.
Sabena's debts total about 2bn euros (£1.2bn; $1.8bn).
Virgin hope falls through
Earlier on Tuesday, Virgin Express, the budget airline part-owned by the British tycoon Sir Richard Branson, said it had failed to cut a deal to buy parts of Sabena's operations.
Virgin Express had hoped intensive last-ditch talks on Tuesday would bring an agreement but eventually dismissed the proposals on the table as "inoperable".
But by late-morning it said it now believes "it will be in the best interests of Virgin Express to pursue (an) independent plan".
It intends to increase its own flights from Brussels.
Any bailout for Sabena has focused on restructuring the airline around its Delta Air Transport (DAT) subsidiary which flies 100-seater jets to European destinations.
Brussels airport chaos
There were chaotic scenes in Brussels' Zaventem airport as flight authority officials warned travellers holding Sabena tickets to stay away.
"No one knows what's going on," said check-in counter worker Trudi Weerts, who described the confusion as "scandalous".
Nevertheless, the government is thought to have drafted extra police at Zaventem airport to deal with possible disturbances.