The drama follows a slew of dramatic interest in the heist, after two films and a radio play about how the thieves broke into the vault.
Larry Lamb and Phil Daniels starred in a big screen version released in April, while Michael Caine and Ray Winstone will star in another upcoming film.
A cartoon also appeared on the BBC News website last year.
Six men were jailed for up to seven years for stealing items from the vault in central London in 2015, with an estimated two thirds of the valuables still unrecovered.
The robbery took place in London's diamond district, carried out by a gang of career criminals who drilled three 25cm holes through a concrete wall to climb into the vault.
Spall, who won best actor at the 2014 Cannes Film Festival for Mr Turner, will star alongside Kenneth Cranham in four 60-minute episodes.
Jeff Pope, ITV Studios' head of factual drama, said: "This is one of the most high-profile crimes of the last decade and we wanted to understand what had happened - and why it had happened.
"The research threw up some fascinating detail and blew away many of the misconceptions about this story. It was not about a bunch of 'loveable old blokes', many box holders lost everything in the raid and we will reflect this.
"But the planning was clever and the characters involved unique."
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Alan Wood, 50, was bound and tortured in his home in Lound, near Bourne, in October 2009.
Det Supt Stuart Morrison, who has led the investigation from the start, said he thinks about the case every day.
He said the main focus of the inquiry was to find the person whose DNA profile was left at the scene.
Det Supt Morrison said the profile was not in the UK database and officers were continuing to check international databases.
He said he had taken guidance from Professor Sir Alec Jeffreys, the pioneer of DNA profiling, as to whether it would be worth trying to trace which country the person who left the DNA at the murder scene came from.
"Whilst there are companies that will seek to tell you that information, it's not particularly reliable and it covers so many countries that it would be of no particular practical use for us," the detective told BBC Radio Lincolnshire.
Mr Wood, who ran a small gardening business, had no known enemies, according to Lincolnshire Police.
He was subjected to a "brutal and sustained" attack at his home in Lound, during which he had his throat cut a number of times and an attempt was made to decapitate him.
"I have to be optimistic that this person or people will be found. It's an investigation that I turn over in my mind every single day.
"It is something that you want to do [solve the case] for the victim and for the family, so we occupy quite a lot of our time thinking about it," Det Supt Morrison said.
Manor Lodge, where Mr Wood lived, was kept as a crime scene for two years but has recently been demolished.
Timothy Spall is to star in ITV's dramatisation of the Â£25m Hatton Garden safety deposit box jewellery raid.
[NEXT_CONCEPT]
The detective leading an inquiry into the brutal murder of a Lincolnshire man has said he remains determined to bring those responsible to justice.