It happened yesterday (Wednesday) at about 6.50pm as the ambulance flew back to their Nostell Air Support Unit base after completing a mission.
The illegal drone was flying at around 1,300ft and almost crashed into the HMN98 helicopter.
The ambulance missed the drone by just three metres.
Steve Waudby, the chief pilot, said the situation but the pilots in "extreme danger" and the consequences of the drone "don't bear thinking about."
He said: “We cannot stress enough the seriousness of what happened last night to the crew of HM98. It was only due to the vigilance of our front seat paramedic spotting the drone, and the rapid reaction of our pilot that the crew avoided a direct collision.
"It is estimated that they missed the drone by less than 3 meters in the end. The consequences don’t bear thinking about if a direct strike had occurred. We’d be telling a very different story today if it had.
“The most ironic thing about all of this is that we spent most of yesterday working with the Civil Aviation Authority (CAA) over at Nostell to help them create a new ‘Drone Awareness’ short film to help highlight the dangers & issues of operating drones, and to make users more aware of aircraft operators like us and the Police.
“Whoever was operating this drone was doing so at an illegal height – the maximum height it should have been operating at was 120m or 400ft, so as you can see, this drone was flying over 3 times the height it should have been at.
Whether the operator is aware or not, they have put the lives of our crew in extreme danger."
Mr Waudby also appealed to the operation to come forward and said that they have a "very clear" description of what the drone looked like as it was "very, very distinctive."
Peter Sunderland, Chairman of the YAA, said a crash would have been an "unthinkable disaster."
He said: “Firstly I would like to pay tribute to our Pilot – his prompt and professional actions avoided the most unthinkable disaster.
"We are proud to have a team of highly skilled, ex-military Pilots as part of our team, and last night’s incident just goes to highlight how important these professional Pilots are to the Charity. Also to the two paramedics and Doctor who were on board – all of their intense training over the years came to fruition last night and I am proud of how they handled this incident.
"The crew are obviously shaken from what happened and we will be supporting them in any way we can.”
A Civil Aviation Authority spokesperson said: “It is against the law to fly a drone above 400ft (120m) or close to airports without permission and anyone flouting the rules can face severe penalties including up to five years in prison.
"Anyone operating a drone must do so responsibly and observe all relevant rules and regulations. The rules for flying drones are designed to keep all airspace users safe. The CAA’s Dronecode provides advice on how to fly your drone safely and follow the rules."
Police have been notified about the incident.