Mr Combe and Mr Patterson Gardner were the only two on board the aircraft. Both were declared dead at the scene.
In a statement, the company said both men were staff members.
"We would like to express our deepest condolences to friends and families of both members on board and are devastated by the loss of such valued and highly regarded team members," the statement said.
"We would like to sincerely thank the emergency services for their incredible effort and assistance this afternoon.
"We are working with police and other external authorities to conduct a full investigation."
In 2012, Mr Combe was given a safety accolade from the New Zealand Helicopter Association, according to Over The Top Helicopter's website.
The next of kin of both men had been notified, and victim support staff brought in to to assist the families, police said.
"It is too early in the investigation to speculate as to possible causes for the crash," Detective Sergeant Brian Cameron of Queenstown police said.
"Police are working closely with the Civil Aviation Authority (CAA) and the Transport Accident Investigation Commission (TAIC) in order to determine what has occurred."
Staff from both agencies were due to arrive in Queenstown early tomorrow to meet police, he said.
It was anticipated that a detailed scene examination would take place after their arrival.
"The deaths of the two men have been referred to the coroner and post mortem examinations will occur tomorrow at Christchurch," Mr Cameron said.
The TAIC said it had opened an inquiry into the fatal crash.
"Two investigators have begun work this evening gathering background information," it said in a statement.
"Tomorrow morning they will travel to Queenstown to meet with police and the aircraft company involved, before travelling by helicopter to the accident site to examine the wreckage.
"The commission's inquiry will aim to establish what happened and why, and if anything can be done to help prevent a similar recurrence."
Keith Allen of the Rescue Coordination Centre New Zealand (RCCNZ) said up to three helicopters from Queenstown and Wanaka were involved in the search for the missing chopper.
"This is obviously a tragic outcome and our thoughts are very much with the families of those involved," he said.
The helicopter's distress beacon had not been activated, RCCNZ spokesman Steve Rendle said.