A 58-year-old from Gosport and a 65-year-old from Bulls Cross, London, were killed in the incident north of Goodwood Aerodrome at about 4.38pm on Wednesday, Sussex Police have said.
Officers are providing support to the men’s families.
Another pilot took off from the same airfield just before the plane involved in the crash.
He said: ‘Shortly after I took off another plane took off, as I was coming into land I was told to land and other air traffic was told not to enter the airport air traffic zone.
‘I could see black smoke reaching 100ft at the other side of the runway just outside the bounds of the airfield itself.’
The pilot added that he estimated the aircraft took off at between 4.20pm and 4.30pm.
There was speculation among amateur pilots on social media that the crash may have been caused by the aircraft’s engine stalling just after take off.
The Air Accidents Investigation Branch (AAIB) is looking at the nature of the crash to determine what happened.
A spokeswoman said: ‘A team of inspectors are continuing to work on site to investigate the circumstances that led to a light aircraft crashing shortly after takeoff from Goodwood yesterday.’
West Sussex Fire and Rescue Service also attended, and were still on the scene on Thursday.
They are pleading for people to keep away from the area while emergency service personnel are on-site.
A spokesperson for the fire service said: ‘We were called to reports of an incident involving a light aircraft off New Road near Chichester at 4.38pm this afternoon.
‘Joint Fire Control mobilised a crew from Chichester Fire Station along with the service's Technical Rescue Unit to the scene.
‘Our crew booked away from the scene at 5.29pm, but members of the public are urged to avoid the area for the time being to allow emergency service staff to work safely.’
Terry Coombes, from the Daedalus Aviation and Heritage Group at Solent Airport in Lee-on-the-Solent, said it was a ‘very sad day’.
A spokeswoman for Goodwood, the company that runs the West Sussex airfield, said: ‘Sadly, there was an aircraft incident near the Goodwood Aerodrome yesterday afternoon and two people tragically died.
‘Our thoughts are with their families and friends at this very difficult time.
‘The Air Accidents Investigation Branch are conducting their investigation at the scene, which is ongoing.’