Choudary, now 50, was jailed for five and a half years in September last year for urging Muslims to support the Islamic State. The judge in his ruling then said that the "calculating and dangerous" man should be locked up behind bars.
AmongChoudary's followers was one of the five attackers who stormed a cafe in Bangladesh capital Dhaka in July last year and killed 22 people, including an Indian girl.
Choudary has become the first known Islamist to be moved to a "separation centre" at HMP Frankland, a high-security prison in County Durham, northeast England, The Sunday Times reported.
He was moved to the unit after he refused to stop preaching his extremist views despite being warned by prison authorities, the newspaper reported.
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Frankland's separation centre is the first of three in high security units. The other two are Woodhill, in Milton Keynes, which is expected to open in September, and Full Sutton, in Yorkshire.
But he added: "The possibility of hope and change is important, not just as a moral abstraction but because it will keep staff and prisoners safer."
The Ministry of Justice has refused to officially identify prisoners in Frankland's separation centre.