Ten people died after a Police Scotland helicopter crashed onto the bar in Glasgow city centre in November 2013.
A preliminary hearing will take place on Wednesday 3 October at Hampden Park in the city, where the inquiry will be held.
Further preliminary hearings are due to follow on 4-5 December and 5-6 February.
The main inquiry is due to get underway on Monday 8 April.
Thompsons Solicitors, which represents, the families of two of those who died and many of the 31 injured, said: "It has taken far too long for us to reach this stage."
Pilot David Traill and crew members Constable Tony Collins and Constable Kirsty Nelis aboard the helicopter were killed along with seven customers of the bar.
The Crown Office said: "The Crown Office and Procurator Fiscal Service (COPFS) can confirm the process to initiate a fatal accident inquiry into the Clutha helicopter crash has begun.
"COPFS appreciates the importance of this inquiry to those affected, and we have informed them of this development."
It was announced in November last year that an FAI would be held, with some victims' families critical of the time taken for a decision to be made.
More than 100 people were at the Clutha Vaults pub when the helicopter, returning to its then base a mile to the west, crashed.
Seven customers died - John McGarrigle, Mark O'Prey, Gary Arthur, Colin Gibson, Robert Jenkins, Samuel McGhee and Joe Cusker.
An UK Department for Transport air accidents investigation branch report published in 2015 found two fuel supply switches were off and the pilot did not follow emergency procedures after a fuel warning in the cockpit.
The Crown Office has previously stated there is insufficient evidence for criminal proceedings.
Patrick McGuire, a partner with Thompsons Solicitors, said: “This is very welcome news from the Crown Office, although it has taken far too long for us to reach this stage.
"An FAI is the only way the families of those who lost their lives will be able to learn what happen to their loved ones on that awful night almost five years ago.
"The FAI will also be able to make recommendations that will hopefully prevent a similar accident from happening again.
"I hope the Crown Office will make sure the families are at the very centre of this process, are kept fully informed of all developments and are treated in a compassionate and sympathetic manner.”
However, Paul Kavanagh, of KM Law, who represents the families of five of those who died in the pub and its owner, said: “They are more concerned about the lack of information coming from the Crown.
"This is in marked contrast to the M9 deaths, where the Crown kept the families up to date on a monthly basis."
Mr Kavanagh said he was not concerned about the time taken for the FAI to start.
He said: "The Crown must have learned from their actions in the Glasgow bin lorry case [in which six people were killed in 2014].
"The FAI [which reported within a year of the crash] was rushed and it was a disaster
"Justice rushed is justice denied."
A Crown Office spokesperson said: “The investigation by the police, with officers working closely with our helicopter team has necessarily been wide ranging.
"It has involved the collection and consideration of a significant volume of documentation, including highly technical manuals and guidance, as well as the taking of detailed statements from witnesses, including professionals in the aviation industry.
"Some of that material and information has been gathered from organisations based abroad.
“COPFS appreciates the wait for a decision regarding proceedings must have been extremely difficult and stressful for those affected and we will keep them informed of significant developments.”