Nasserdine Menni was found guilty of supporting suicide bomber Taimour Abdulwahab, who blew himself up in a blast in Stockholm in December 2010.
A worldwide investigation uncovered Menni's links to Muslim extremist Abdulwahab.
Menni, believed to be in his early 30s, had previously claimed asylum while in Glasgow and it was money earned in the city from benefits and low-paid jobs that was intended to help carry out a mission to kill innocent citizens.
He was locked up for seven years in August 2012 for providing £6725 in the knowledge it could be used for terrorism.
His legal team, led by the same QC who defended the Lockerbie bomber, yesterday challenged the jail term at a Court of Appeal hearing in Glasgow.
Lord Gill, the Lord Justice General, sitting with Lords Menzies and Brodie, reduced the sentence to three years and backdated it to March 2011 when Menni was taken into custody.
It meant Menni had effectively served his sentence.
But, it is thought Menni, who arrived at court from Low Moss Prison, Bishopbriggs, East Dunbartonshire, will not be freed while he awaits being deported from the UK.
In a bizarre incident before leaving the dock, Menni appeared to react angrily and shout at the appeal judges.
It later emerged this came about after a mix-up with his interpreter led to him thinking three years was being added to his jail term rather than it being cut.
A bid to overturn the conviction had previously been rejected by appeal judges.
During his trial at the High Court in Glasgow in 2012, a jury heard how Menni's links to Taimour Abdulwahab emerged following an inquiry after the bombing in Sweden.
Abdulwahab, an Iraqi-born Swedish citizen, killed himself on December 11, 2010 in an explosion in the city centre of Stockholm.
A £910 Audi car he bought had initially been set alight, but the devices inside, including a pressure cooker filled with explosives, failed to detonate.
Two people were hurt, but many lives were likely saved due to a loose wire on a device.
Abdulwahab and Menni had previously forged a bond amongst the Arabic community living in Luton, Bedfordshire.
The police and the security services began to piece together Menni's background.
He arrived in Britain about 2002 and eventually got a £17,000-a-year job making car seats.
He worked there under the name Emmanuel Philip Bernard, having purchased false identity documents.
But in April 2009 Menni disappeared without alerting his bosses. It emerged he had gone to Liverpool claiming asylum, pretending to be a Kuwati citizen named Ezeeden Al-Khaledi.
Menni then ended up in Glasgow, initially living in the city's Red Road high-rise flats, and working in restaurant kitchens.
Prosecutor Andrew Miller told the trial: "It was a dramatic change. The effect of the asylum claim was to create distance between himself and Abdulwahab and provide financial support. He had a new identity and was able to falsely claim benefits."
Menni deposited amounts totalling £5725 which helped pay for Abdulwahab's trips abroad for the "purposes of Jihad".
Another £1000 was sent intended for Abdulwahab's wife after his death.
Menni's lawyers claimed there was nothing sinister in the money that was given.