Passengers were trapped for hours on the tarmac as they waited for ground staff to deal with the incident.
In spite of facing a further four hours' delay, the easyJet passenger said he was "just happy everyone is OK."
KLM's passengers bound for Madrid were put on a replacement plane, with apologies.
Both aircraft involved in the incident were removed from service, pending mechanical inspection.
"EasyJet can confirm that two aircraft made contact during pushback from stand, one of which was easyJet flight EJU8868 from Amsterdam to London Gatwick," read a statement from easyJet.
"Passengers have now disembarked into the terminal where they have been provided with updates and refreshment vouchers. The flight is now due to be operated by a replacement aircraft."
"The safety of its passengers and crew is easyJet's highest priority and an investigation has been launched in line with procedure to understand what happened."
The Dutch flag carrier KLM tweeted news of the incident, saying: "This morning a KLM Boeing 737-800 hit another aircraft during the pushback at the gate. The passengers were not in danger and were taken off board. After a delay of 2.5 hours the passengers left with another aircraft. It is being investigated how the situation could have arisen."
Schiphol airport is Europe's third busiest airport, transporting 71 million passengers a year on almost half a million departures. KLM accounts for almost half of the air traffic as the headquarters for Royal Dutch Airlines KLM.
