US Attorney General John Ashcroft, Homeland Security Secretary Tom Ridge and FBI Director Robert Mueller are all named in the lawsuit.
Maher Arar, a Syrian-born Canadian, was returning from a holiday in Tunisia in 2002 when he was arrested in New York.
He was deported to Syria, where he was held for 10 months.
The US Department of Justice has said it has information that Mr Arar is a member of Osama Bin Laden's al-Qaeda network and remains "a threat to national security".
Mr Arar, now 33, was arrested while changing planes at New York's John F Kennedy airport in September 2002.
He alleges that while in US custody he was not afforded even basic rights.
"From the moment I was held in the United States I was treated as though I was a convicted terrorist," he said at a news conference in Ottawa on Thursday.
"I endured hours of interrogation. I was chained and shackled."
After almost two weeks Mr Arar was deported to Syria, not Canada.
The lawsuit says US officials knew that the country was practising torture.
He was released after 10 months in a Damascus prison, where he says he was beaten with cables and forced to sign a confession linking him to al-Qaeda.
Mr Arar says he is not asking for a specific amount of money, leaving that to the courts. The most important thing is to clear his name and show he is not a terrorist, he insists.
In Canada, the case has led to an inquiry into the possible role of intelligence officials in the deportation.