The boys, aged 10 and 11, who both attend Warleigh School, near Bath in Avon, which caters for children with behavioural difficulties, were later returned to the care of their teachers.
A Foreign Office spokesman said: "Spanish police reported to us that two boys were detained in the early hours of this morning after a chase on the luggage conveyor belts.
"They had earlier been discovered driving a stolen airport authority vehicle on the runway of Reina Sofia airport in the south of Tenerife." He added that Spanish police had said that there would be no charges.
"As soon as we heard about the incident, they were visited by the vice- consul in Santa Cruz at the airport police station. They were found to be healthy but quite tired."
However, last night, the principal of Warleigh School, Leslie Alderman, said that there was no indication that the children had been in- volved in a high-speed chase at the airport.
Mr Alderman, who was leading a party of 10 children and five members of staff on the holiday at Arona in Tenerife, said the boys disappeared after a trip to a concert.
"I am amazed at the furore this small incident seemed to have caused in England," he said. "The concert began at 9pm and all boys were present and accounted for at 10.57pm when we decided to leave.
"We walked in a group back to the hotel and at 11.05pm it was discovered that the two boys were missing.
"The whole group retraced our steps but could not find the 10-year-old and 11-year-old. Our concerns were such that we informed the Guardia Civil at midnight."
Mr Alderman said teachers scoured the streets of the town looking for the boys before visiting Tenerife airport at 3.30am.
He added: "There were no police, no airport staff and no indication that our boys had been there.
"This morning, my staff again visited the airport and were told that the boys had been found and taken to the police station in Playa de las Americas. At the police station my staff were informed that the boys had in fact been taken to the police station at Santa Cruz, some 70 kilometres away.
"I and a member of my staff went immediately to Santa Cruz. I was informed by a senior police officer from the bureau for minors that the boys had not been arrested.
"They had not been charged with any offences, they had simply been taken into protective custody for their own safety as they were minors, lost and obviously had some form of learning difficulty.
"She informed me that the British Consulate was not involved, that the boys had hidden behind a car and that there was no allegation that there had been a high-speed car chase across the airport involving Warleigh school boys."