Roberts, now 78, was handed a life sentence in 1966. His 30-year minimum tariff expired 18 years ago.
The funeral of murdered schoolgirl Alice Gross will take place today.
The 14-year-old's body was found in the River Brent in west London on September 30, four weeks after she disappeared.
The prime suspect in her murder, Latvian national and convicted killer Arnis Zalkalns, was found hanged on October 4.
Alice's disappearance sparked an outpouring of support around Hanwell, where the keen musician lived with her parents, Rosalind Hodgkiss and Jose Gross, and elder sister, Nina.
Residents of Hanwell have left tributes and flowers in honour of murdered schoolgirl Alice Gross, whose funeral takes place today.
Harry Roberts opened fire on three unarmed police officers after they pulled over his van ahead of an armed robbery near Wormwood Scrubs Prison in 1966.
The murders of PC Geoffrey Roger Fox, 41, Detective Constable David Stanley Bertram Wombwell, 30, and Detective Sargent Christopher Tippet Head, 25 shocked the nation.
Roberts went on the the run for more than 90 days and was eventually found in Hertfordshire following a huge manhunt.
The judge who jailed Roberts described it was "the most heinous crime for a generation or more", and warned that he could spend the rest of his life behind bars.
But Roberts, now 78, could be released within days after approval by the Parole Board.
The decision to release Harry Roberts is a "slap in the face" for the families of his victims, the head of the police federation said.
In a statement to ITV News, Steve White, Chair of the Police Federation of England and Wales, said he was "appalled" by the Parole Board's ruling, adding that officers felt "badly let down".
Police killer Harry Roberts is to be released from prison after more than 45 years behind bars.
Roberts, now 78, was handed a life sentence for the murder of three policemen in Shepherd's Bush, west London, in 1966. His 30-year minimum tariff expired 18 years ago.
The Parole Board is understood to have approved his release and he will be subject to close monitoring by police and the Probation Service.
Detective Sergeant Christopher Head, 30, Detective Constable David Wombwell, 25, and Pc Geoffrey Fox, 41, were shot dead without warning while questioning three suspects in a van on August 12, 1966.
A Ministry of Justice spokesman said: "We do not comment on individuals.
"The release of life sentence prisoners is directed by the independent Parole Board once they are satisfied they can be safely managed in the community. Once released they are subject to strict controls for as long as their risk requires them. If they fail to comply with these conditions they can be immediately returned to prison.
"Offenders managed through Multi Agency Public Protection Arrangements (MAPPA) are monitored and supervised by probation, police and other agencies."
On the day George Osborne held talks with the NFL about basing an American Football team at Wembley, it seems one side still has a lot to learn.
The Atlanta Falcons take on the Detroit Lions in London this weekend. But just take a look at this map made to help fans get to the capital.
Point 3 on the map is definitely not London. Scotland also appears to have been re-shaped. Luckily the team spotted the mistake, and have produced a more accurate guide here.
Three NFL games are taking place at Wembley this season, bringing in an estimated revenues of £3 million per game, and previous games at the national stadium have been played in front of strong crowds.