"All military operations have come to a stop," army chief Lieutenant General Sarath Fonseka said in a statement after troops overran the last sliver of Tiger territory.
"Now the entire country is declared rid of terrorism," Fonseka said.
"Over 250 dead bodies of terrorists are scattered over the last ditch.
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His statement marked the end of one of Asia's oldest and most brutal ethnic conflicts which left more than 70,000 dead from pitched battles, suicide attacks, bomb strikes and assassinations.
The Liberation Tigers of Tamil Eelam (LTTE) emerged in the 1970s, with all-out war breaking out in the early 1980s in their struggle for an independent Tamil homeland.
The victory declaration came shortly after news broke that LTTE supremo Prabhakaran had been shot dead in the final offensive.
A senior defence ministry official told AFP that Prabhakaran and his two deputies had tried to flee advancing troops in a small convoy when it was ambushed by commandos.
"He was killed with tw