The helicopter, owned by a Nigerian businessman, was being used to shuttle the Togolese officials to the airport after winning an African Cup of Nations football match 1-0 against Sierra Leone.
The Togo football team was in Freetown awaiting the next shuttle when the accident took place.
Airport authorities said a total of 22 people were on board the helicopter, while sports officials said they believed there to be only 21 on the flight.
Chernor Ojuku Sesay, the Sierra Leone Football Association's public relations officer, said that "most of the victims were burnt beyond recognition".
The fire from the crashed helicopter was only extinguished after several hours, airport workers said.
"We are deeply moved over this development. We are also grieved by this tragic loss," said Nahim Khadi, president of the Sierra Leone Football Association.