Rugova was a chain-smoker
Mr Rugova, 61, died on Saturday in his residence in the Kosovo capital, Pristina, his spokesman announced.
Regarded as a moderate ethnic Albanian proponent of independence, he came to prominence in the 1990s as leader of the resistance against Serbian rule.
The province's UN administrator said it was "tragic" that Mr Rugova had died days before talks on the Kosovo future - now postponed - were due to start.
He had been leading the Kosovo Albanian negotiating team in the talks despite his illness, and has no obvious successor.
Kosovo has been under UN administration since 1999 when a Nato bombing campaign stopped Serb forces expelling ethnic Albanians during a separatist war.
'Dignity and courage'
The Kosovo president died shortly before midday local time (1100 GMT) in his residence surrounded by his family, said his spokesman Muhamet Hamiti.
"He carried his battle with cancer with great dignity and courage until his last breath," Mr Hamiti told the Associated Press news agency.
The flag at his home was lowered to half-mast on Saturday.
"The best tribute that we can pay to president Rugova and his legacy is to stay united during the coming months," said the head of the UN Kosovo mission Soren Jessen-Petersen.
French President Jacques Chirac called for his legacy to be maintained.
"France pays tribute to the historic role and to the political courage which drove Ibrahim Rugova in defending the democratic rights of the Kosovar people and in working for the restoration of peace and reconciliation in your region," he said.
Leaders of Serb communities in the region also offered tributes, but said his death was likely to bring instability.
"Rugova was a man with a certain democratic potential and a man who has never been accused of doing anything illegal," nationalist Serb leader Milan Ivanovic said.
"His death will destabilise the situation in Kosovo as I am convinced there will be sharp clashes amongst [ethnic] Albanians."
UN-mediated talks between delegations from Kosovo and Serbia had been due to begin in Vienna, Austria, on Wednesday, but UN spokeswoman Hua Jiang said they would now be put forward to February.
'Father of the nation'
Rugova, a chain-smoker, was officially diagnosed with lung cancer in September 2005.
He had been undergoing chemotherapy treatment at his residence in Pristina, the capital of Kosovo, that left him frail and caused him to lose his hair.
Rugova's non-violent campaign for independence earned him high regard in the international community.
When Serbian President Slobodan Milosevic revoked Kosovo's autonomy in 1989, Rugova founded the Democratic League of Kosovo (LDK), which created its own system of hospitals, schools and taxation, boycotting the Serbian administration.
It gave him "father of the nation" status among some Kosovo Albanians.
But analysts say there is no clear successor in the Democratic League of Kosovo, and there could be a power struggle.
Rugova's main rivals came from the paramilitary Kosovo Liberation Army that fought Serb troops.The head of parliament, Nexhat Daci, is expected to be named acting president until a new leader is chosen by parliamet. BBC
Update: Kosovo news Agency KosovaPress reports the government of Kosovo and the Parliament have decided that the President will be buried on Wednesday, Jan 25th.