Kray, 63, was given a life sentence in 1969 for killing Jack "The Hat" McVitie, who was stabbed to death. His 30-year "life" tariff expires in May next year and his supporters hope he will be granted parole.
He was moved from the high security Maidstone prison to the low security, category C jail at Wayland in Norfolk, where he will be offered offender behaviour programmes and "enhanced thinking" training.
If he is no longer considered a risk to the public he could then be released under licence.
His new wife, Roberta, said: "This is one step closer to his eventual release, the first glimpse of light at the end of a very long tunnel."
Kray and his twin brother, Ron, ran one of the most feared gangs in Britain during the 1960s from their strong hold in the East End of London. Ron Kray was jailed for life for the murder of gangsters George Cornell and Jack McVitie in 1968 and died of a heart attack in 1995 in Broadmoor hospital.Reuse content