The sentence follows his conviction last month on charges that include espionage.
Officials did not give details about the sentence but said in a statement it included jail time.
Jason Rezaian, 39, has been detained in Iran for more than a year. The Post has dismissed the charges as absurd.
"In brief, it is a prison sentence," judiciary spokesman Gholamhossein Mohseni Ejei said in a statement on Iranian state TV.
He added that the verdict is "not finalised" - referring to an expected appeal.
Rezaian's lawyer, Leila Ahsan, told the Associated Press news agency she had not been informed of the verdict or the details of the sentence.
The foreign editor of the Washington Post, Douglas Jehl, said in a statement that Rezaian's "trial and sentence are a sham, and he should be released immediately". He added that the journalist had already spent 487 days in prison.
Rezaian, his wife, who is also a journalist, and two photojournalists were arrested in July 2014 in Iran. Rezaian was the only one of the group not to be released.
The Post's Tehran bureau chief since 2012, he was charged with espionage and distributing propaganda against the Islamic Republic.
He is a dual Iranian-American citizen and was tried in four hearings behind closed doors. He was convicted in October.
Earlier reports said Rezaian could face 10 to 20 years in prison.

Bakir Izetbegovic, a member of Bosnia's tripartite presidency, said he was seeking "truth and justice".
Bosnian Serb officials warned the move would trigger a "serious crisis" in the country.
In 2007, the International Court of Justice (ICJ) cleared Serbia of direct responsibility for genocide.
The ICJ found only one act of genocide during Bosnia's 1992-95 war - the massacre of about 8,000 Bosnian Muslim (Bosniak) men and boys by Bosnian Serb forces in the town of Srebrenica in 1995.
It was Europe's worst atrocity since World War Two.
The ICJ ruled that Serbia had violated international law by failing to prevent the killings, but absolved it of direct responsibility.
On Thursday, Mr Izetbegovic told reporters that "the request [for a review] is being submitted at this very moment".
"I think that I am on the path of truth and justice," he added.
The appeal was launched before a 10-year deadline expires on 26 February.
Mladen Ivanic, the Serb member of the presidency, said the move should have been made collectively by the tripartite body, where a Bosnian Croat also has a seat.
"I am afraid that we have entered a really serious crisis," Mr Ivanic said.
Meanwhile, Serbia Prime Minister Aleksandar Vucic earlier described Mr Izetbegovic's intentions as "bad" for relations between the two countries.
Following the 1992-1995 war, Bosnia is now an independent state under international administration.
Its three main ethnic groups are Bosniaks (Bosnian Muslims), Croats and Serbs.
Politicians from Bosnia's two semi-independent entities - the Muslim-Croat Federation and the Republika Srpska - have often clashed, triggering political crises.
The powers of the central government in the capital Sarajevo are very limited.
Washington Post reporter Jason Rezaian has been sentenced to an unspecified prison term in Iran, the country's judiciary has said.
[NEXT_CONCEPT]
Bosnia has formally asked the UN's top court to review its ruling which cleared Serbia of genocide in the 1990s, Bosnia's Muslim leader has said.