The verdict risks a further escalation of tensions with Saudi Arabia's minority Shiite community.
Nimr was a driving force behind demonstrations against the Sunni authorities that erupted in 2011 in the oil-flush east, alongside a Shiite-led protest movement in neighbouring Bahrain.
The cleric was also convicted of seeking "foreign meddling" in the country, a reference to Iran, his brother Mohammed al-Nimr wrote on Twitter.
He was found guilty of "disobeying" the kingdom's rulers and taking up arms against security forces, his brother said.
"The ruling... Is political par excellence," his relatives in the Eastern Province communities of Awamiya and Qatif said in a statement.
They called for a dialogue with officials, "out of concern for our dear country".
Nimr, who is in his 50s, had been on trial since March 2013.
Amnesty International slammed the verdict as "appalling," dismissing Nimr's trial as "deeply flawed," and calling for the sentence to be immediately quashed.
The sentence is part of a campaign by the authorities "to crush all dissent, including those defending the rights of the Kingdom's Shiite Muslim community," said Amnesty's Said Boumedouha.
A diplomatic source said the sentence would trigger " a lot of anger".
But whether that would translate into renewed street protests was hard to say, said the source, requesting anonymity.
Most of Saudi Arabia's estimated two million Shiites live in the east, where the vast majority of the wealthy kingdom's oil reserves lie, and many complain of marginalisation.
They began demonstrating in February 2011 after an outbreak of violence between Shiite pilgrims and religious police in the Muslim holy city of Medina in western Saudi Arabia.
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