Syed Talha Ahsan, 34, from Tooting, south London, was sentenced last month in Connecticut for aiding terrorists.
His brother Hamja Ahsan said it was "really cruel" he was still being held by the US authorities.
The Foreign Office said it was aware of the case and was providing consular assistance to Ahsan.
"This is the eighth year in a row where we have not had Talha home for Eid and it was really cruel that he could not be brought home, even though he was set free weeks ago," Mr Ahsan's brother said.
"I get messages from people around the world asking why Talha is still in custody if he is now a free man."
Ahsan, who has Asperger's syndrome, was extradited to the US in October 2012 after spending six years in high-security prisons in the UK awaiting a trial.
He was never charged in Britain, but US prosecutors accused him and Babar Ahmad, from Tooting, of running a pro-jihadist website.
The now defunct site, Azzam, was operated from London but hosted on US internet service providers.
Ahmad and Ahsan admitted conspiracy and providing material to support terrorism as part of a plea bargain agreement with the US Department of Justice.  Ahmad was jailed by a US court last month.
However, Ahsan and his family say he is not a terrorist.
Hamja Ahsan said that his brother was being held at at Franklin County Jail in Greenfield, Massachusetts.
"Talha had little choice but to enter a plea bargain: he was faced with the option of dying in a 'supermax' prison, or entering into a plea bargain, which was the quickest way to come home," he said.
His mother Farida Ahsan said: "The last time I saw him was before he went to the US.
"I'm very anxious for my son to come home. Until I see him I will be waiting anxiously."
The Foreign and Commonwealth Office said it was aware of a British national in custody in the US and was continuing to provide consular assistance to Ahsan and his family.
The US Department of Justice has not commented.
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A British man sentenced by a US court to time already served after admitting terrorism offences has still not been released, according to his family.