Arunachalam Chrishanthakumar, 52, was found guilty of coordinating supplies of material to the Liberation Tigers of Tamil Eelam (LTTE).
Jurors failed to reach verdicts on three other charges against Chrishanthakumar, also known as AC Shanthan, plus one charge against another accused, Jegatheeswaran Muraleetharan.
Chrishanthakumar, described as a "very prominent figure" in Britain's Tamil community, supplied electrical components for the LTTE, some of which had "an obvious terrorist purpose," the court found.
He was also convicted of receiving documents for the purpose of terrorism, after a trial at Kingston Crown Court, southwest London.
The LTTE has been fighting to carve out an independent homeland for the Tamil minority in north and east Sri Lanka since 1972.
Tens of thousands have died on both sides of the conflict in the Sinhalese-majority nation.