The men, dressed in dark clothing, jumped from the cockpit and ran towards a hangar where they met police. They were then taken to the medical centre, where they received medical treatment and were interviewed.
The lights of the cabin and cockpit remained on after the escape. "We are talking to people on board, and they are calm," an Essex police spokeswoman said last night.
It was not immediately clear whether the men were crew, hostages or - thought less likely - members of the hijack gang itself. Police said hijackers remained on board.
The development took police by surprise after a day of slow but ordered negotiations with the hijackers, which had seen the release of just one of the remaining 157 Afghan passengers on the plane. Eight had been freed on Monday.
Shortly before the escape the plane's cabin lights were switched on, having been switched off for 45 minutes. Police said it had been a spontaneous escape.
Armed police had spent the day situated about 50 yards from the plane in a south-east corner of the airfield.
Mike Ganes, an aviation expert, said last night that the four men who escaped could have used emergency ropes that are placed in the cockpit to help descent from the plane.
The men were seen to clamber out through the window before sliding down the side of the plane's cockpit to make the 20ft drop to the runway tarmac. They were then seen to run towards a hangar where police have been based during the standoff.
Essex police said last night their first concern, as it had been throughout the hijack situation, was for the safety of the passengers on board. It was unclear immediately whether the men who had escaped were hostages or hijackers who had perhaps split from the others over differing opinions.
A police spokeswoman said early today: "It appears to have been an escape of four people. We are gauging what effect this has had on the other people on board. We are talking to people on board as we speak. Everything appears to be calm. We have no more information at the moment."
After the escape, activity around the plane intensified, with an airport bus seen to pass close to it. It was not clear if it had been dispatched to pick up the four men.
Before the dramatic escape last night, a representative of the UN High Commission for Refugees had arrived at Stansted. Joe Edwards, assistant chief constable of Essex police, told a press conference that the unnamed female UN representative had observer status and was not there as a negotiator.
Talks with the hijackers are continuing to be conducted through Essex police negotiators. Because of the "delicate nature of negotiations" police would not reveal why the representative had arrived or who had asked her to come.
But the announcement added to speculation that the hijackers are seeking political asylum.
The UN spokesman John Mills, speaking from New York, said the UNHCR woman at the hijack scene was the organisation's leading representative in the UK.
Mr Mills said: "The UN has no direct involvement in the negotiations. The UNHCR person is there on standby as a representative of a neutral humanitarian organisation."
He would not say who, if anyone, had requested her presence but said the woman, who is based in London, had intimate knowledge of the situation in Afghanistan and should be able to provide the authorities with valuable background information.
