Officials did not give details of the judgement, but hinted at a conviction.
A judiciary official said late on Sunday that the verdict could be appealed, suggesting Mr Rezaian had been found guilty.
Jason Rezaian, 39, has been detained in Iran for more than a year. The Post has dismissed the charges as absurd.
Appearing on state TV on Sunday, judiciary spokesman Gholamhoseyn Mohseni-Ezhei said: "He [Jason Rezaian] has been convicted, but I don't have the verdict's details."
He added: "The time for an appeal is not yet over. So the court waits and if it doesn't receive an appeal... the verdict becomes final."
Mr Mohseni-Ezhei said Mr Rezaian and his lawyer were eligible to appeal the conviction within 20 days.
The Washington Post foreign editor, Douglas Jehl,  called the ruling "vague" and said it was unclear if Mr Rezaian had been sentenced.
"We've now heard from the Iranian government today's [Sunday] announcement that a verdict has been issued in Jason's case, but that it's not final and that it's subject to appeal.
"That's really all we know, and unfortunately it reflects a continued pattern of mystery, opacity and gamesmanship surrounding the way Iran has handled this case.
"The only thing that's been clear from the beginning is Jason's innocence. Everything else has been under a real shadow of darkness."
Mr Rezaian faces 10 to 20 years in prison.
Mr Rezaian, his wife, who is also a journalist, and two photojournalists were arrested in July 2014 in Iran. Mr 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, the last of which was held in August.
A verdict has been issued in the trial in Iran of Washington Post reporter Jason Rezaian on charges including espionage, Iran's judiciary has said.