Arunachalam Chrishanthakumar, 52, was sentenced at London's Old Bailey for illegally procuring equipment for the Sri Lankan group.
He had been convicted of receiving electrical components for terrorism and receiving documents for terrorism.
Three other men who had been tried alongside him were cleared.
Jonathan Laidlaw QC, prosecuting, said Chrishanthakumar procured equipment for the Tigers with an "obvious terrorist purpose".
Mr Justice Saunders said: "This was a protracted, deliberate breaking of a law. These are very serious offences which warrant substantial sentences.
"The terrorist law has to be obeyed as part of our obligations internationally."
The judge said the case was exceptional because, at the time the offences were carried out, the Tamil Tigers were not a banned group in Sri Lanka because of the ongoing peace talks with the Sri Lankan government.