Rezaian, who covered Iran for the Post, has been undergoing a closed trial on espionage-related charges -- charges his family and employer emphatically deny.
"In a year's time, no evidence has been produced of espionage or any other offense," Washington Post Executive Editor Marty Baron told reporters at a press conference Wednesday. "It is clear, as it has been all along, that Jason did nothing wrong. All he did was work diligently and fairly as a journalist."
"Every aspect of this case -- his incarceration, his trial, the conditions of his imprisonment -- has been a disgraceful violation of human rights and it violates common decency," Baron added.
The petition has been filed with the UN's Working Group on Arbitrary Detention, part of the Human Rights Council.
Since his detention, according to the petition, Rezaian has been deprived of his right to due process and been treated inhumanely, subjected to solitary confinement and interrogations.
According to Washington Post General Counsel Jay Kennedy, who also spoke at Wednesday's press event, the petition "makes clear that Jason's detention is arbitrary and unlawful under both Iranian and international law."
"Given the complete lack of evidence that Jason has committed any crime, we expect the working group to conclude, as we have, that the government of Iran arrested and detained Jason for his work as a journalist, and to find that detention completely unlawful," Kennedy went on to say.
The petition comes just one day after the UN Security Council approved a deal between Iran, the United States and other world powers that will ease crippling sanctions on Iran's economy in exchange for curbs on the country's nuclear program.
Rezaian's brother Ali spoke about that vote on Wednesday.
"This agreement was approved by the UN Security Council with little opportunity for review less than a week after it was announced," he said, "yet Jason remains in prison after 365 days held on clearly manufactured charges by parts of the Iranian government that are uninfluenced by Iran's president and hold the rule of law in contempt."
In addition to Rezaian, Americans Saeed Abedini and Amir Mirzaei Hekmati are currently being detained in Iran.
A fourth American, Robert Levinson, went missing in Iran in 2007 and the State Department has said he's believed to be held "somewhere in southwest Asia." U.S. officials have said they believe "the Iranians control his fate."