The paper's Tehran correspondent, Jason Rezaian, is accused of "collaborating with hostile governments" and spreading "propaganda", his lawyer said.
Mr Rezaian was arrested in July and charged in December but the accusations against him were not known until now.
The Washington Post has called the charges "absurd and despicable".
A statement from the paper's executive editor, Martin Baron, accused Iran of "indefensible silence" in having kept Mr Rezaian in jail for nine months without revealing why.
It urged Iran to clear the names of its correspondent and his wife, Yeganeh Salehi, who is also a journalist and was also taken into custody in July.
"The world will be watching; any just outcome to this tragic charade can result only in Jason and Yegi's exoneration and immediate release," the statement said.
The US State Department said the charges against Mr Rezaian, if confirmed, were "patently absurd", Reuters news agency reports.
The US is one of a team of world powers negotiating with Iran over its disputed nuclear programme. It has repeatedly pressed Iran to release Mr Rezaian and other detained US citizens.
Mr Rezaian's lawyer, Leila Ahsan, learnt of the charges after meeting him for the first time on Monday, the Washington Post says.
The charges against him are said to include gathering information about "internal and foreign policy" and providing it to "individuals with hostile intent".
Ms Ahsan said she had not seen any evidence against her client.  She defended him, saying that as a journalist, "it is in the nature of his profession to gain access to information and publish it".
"My client, however, has never had any direct or indirect access to classified information to share with anyone."
Mr Rezaian, a US-Iranian citizen, is being held at Tehran's Evin prison, and is due to be tried at the Revolutionary Court, which hears national security cases. No trial date has been set.
Western news organisations, including the BBC, have difficulty operating in Iran, with journalists facing detention and surveillance.
Iran-based family members of BBC journalists have been questioned by intelligence services, and authorities have tried to intimidate London-based BBC Persian staff.
A Washington Post journalist who was detained nine months ago in Iran is facing four charges including espionage, according to his lawyer.