It said Prabhakaran - along with two of his top commanders - had died while trying to flee from the last rebel-held patch of jungle in the north-east.
The military said it had crushed the Tamil Tigers' 26-year insurgency, as people around the country celebrated.
No photos of Prabhakaran's body have been released. The army says it is working to identify it among the dead.
The claims cannot be verified as reporters are barred from the war zone.
More at BBC here
The BBC's Obituary is here
For a rather long time Prabhakaran has been the God-King of Tamil Elam. His was the ruthless genius that nearly carved out a new Tamil nation from Sri Lanka. He had basically battled the much larger forces of the Government to a stand still. But in the last 24 months or so it all went terribly wrong. Through subterfuge and through naked aggression the armed forces of Sri Lanka have slowly ground the Tamil Tigers into a fine powder.
It has been a brutal affair. The government of Sri Lanka was able get one of Prabhakaran's sub-commander to turn on him, splitting the Tamil Tigers asunder and greatly weakening the military strength of the Tigers. Then the Government proceeded to consistently pressure and attack the Tigers using the superior numbers and logistics of the Army to grind down the Tigers in a slow battle of attrition. Someone in Sri Lanka must have at least glancinly perused the strategies of Grant and Sherman. The willingness to engage the LTE day after day and to keep attacking was definitely like Grant. The bloody-mindedness of the Sri Lankan government caused much hand-wringing in the International community but the pearl-clutching messages delivered by the usual suspects had zero effect. The Sri Lankan Government was bound and determined to put an end to the insurgency that had plagued it for over a quarter century.
Still the downfall of the Tigers may have its actual roots all the way back to the Indian intervention. The Indians originally came as honest brokers and sympathetic to the Tamil cause. The Indians have a strong Tamil representation in the South thus both International and domestic imperatives lead to the Indians deploying to the Island formally known as Ceylon.
Somehow it all went south in a hurry. The specifics of who did what to whom and when are all terribly murky as only politics in South Asia can be. The Indians came to the Island less than enthusiastic in first place, the intervention was mostly Rajiv Gandhi's bright notion and was not all that popular with the domestic Tamils in India as one would suppose. The Indians were ambivalent about the prospect of refereeing the conflict and the Tamils of Sri Lanka made it clear that they were not about to accept any attempt by a foreign power to regulate what they saw as a purely domestic conflict. The Tamils essentially chased the Indians off their island and then blew up Rajiv Gandhi as a parting good riddance gesture. So much for the Indian attempt to impose some kind of reconciliation. The ruling elites in India came face to face with one of Murphy’s Laws : No good deed ever goes unpunished.
Flash forward to the present and it is no wonder that the Indian Government sat on its hands while the government of Sri Lanka ripped into Tamils like a chain-saw though soft butter. The idea of “once bitten, twice shy” translates quite well into all of the languages the Indians might speak. So too does “you made your bed, now lie in it.” It is in that final bed that Prabhakaran now rests.