The inquiry into the death of Greater Manchester Police Chief Constable Michael Todd will look into the possibility he committed suicide.
The 50-year-old father-of-three was found dead near the summit of Mount Snowdon, north Wales, on Tuesday afternoon, his body covered in snow.
He is believed to have killed himself and sources said letters addressed to his family have been found.
A post-mortem examination is taking place at Ysbyty Gwynedd Hospital.
His body has been formally identified by a colleague from Greater Manchester Police.
Mr Todd had been off duty on Monday and had spent the day walking in the Welsh mountains.
The search for him began in the early hours of Tuesday, but it was later in the day that hill walkers reported seeing a body near the summit of Snowdon.
His body was found on part of the mountain called Bwlch Glas at about 1500 GMT.
His body was carried down from the mountain despite poor weather conditions.
Tributes have continued to be paid to Mr Todd, who had been tipped as a future Metropolitan Police Commissioner.
Deputy Chief Constable of Greater Manchester, Dave Whatton, said staff in the force were "absolutely shocked" by the death.
The President of the Association of Chief Police Officers (Acpo), Ken Jones, said: "Mike has made an enormous contribution to policing in Manchester and nationally throughout his distinguished career.
"The news of his death is a tragedy and he will be greatly missed by chief officer colleagues and all who worked with him during his career.
"As a personal friend and valued supporter, I will miss him greatly."
'Decent and committed'
Bernard Hogan-Howe, Chief Constable of Merseyside and Chair of North West Regional Association of Chief Police Officers, also paid tribute to Mr Todd.
"This is a terrible shock. It's a great tragedy for Michael's family and all the people who work with him," he said.
"Michael was a great character, who was full of life and enthusiasm."
Former Home Secretary, David Blunkett, described Mr Todd as a "decent and committed policeman who did a first-class job in difficult circumstances".
"His death is a real tragedy and I personally feel very sad to hear of his loss."
Born in 1957
1976 Trains with Essex Police, moves to Met
1995: Assistant Chief Constable, Notts
1998 Dep Assistant Commissioner, Met
2000: Assistant Commissioner, Met
2001: Queen's Police Medal
2002 Chief Constable, Manchester
2006: Vice chairman, Acpo
Mr Todd was appointed chief constable in Greater Manchester, England's third largest force, in October 2002, following the retirement of Sir David Wilmot.
He had been a police officer for more than 30 years, having joined Essex Police in 1976.
An inquest into Mr Todd's death is to be opened and adjourned at Anglesey Council chamber on Thursday afternoon.
Books of condolence in memory of Mr Todd have been opened at Manchester Cathedral, Trafford Town Hall and Old Trafford Library.
People can also sign an online book of condolence on the Greater Manchester Police website.