Carl Marsh, 46, of Knutsford, Cheshire suffered fatal injuries at Black Knights Parachute Centre in Cockerham, near Lancaster on Saturday.
He was pronounced dead at the scene.
The British Parachute Association (BPA) said the jump Mr Marsh was executing could only have been attempted by an experienced parachutist like Mr Marsh.
Tony Butler, the BPA's chief operating officer, is leading the probe into the death and said it was his "top priority".
He estimated it would take about a month to complete his investigation and he would send his findings to the Civil Aviation Authority, the police and the coroner as well as the BPA's training committee.
Lancashire Police, which is supporting the BPA's investigation, said there were not thought to be any suspicious circumstances surrounding the death.
Mr Marsh's relatives said he was a "much-loved" family man with an "enormous heart".
A parachutist who died performing a jump in Lancashire was attempting a "complicated manoeuvre", the man investigating his death has said.