Ms Parks, who died on Monday, aged 92, will be only the second African American to receive this distinction, allowing visitors to the capital to file past her casket tomorrow as they did for Ronald Reagan's last year.
She became one of the most revered figures of the civil rights era after refusing to give up her seat to a white man on a bus in Montgomery, Alabama, in December 1955. Her subsequent arrest prompted a boycott of local buses that lasted for more than a year, led by Martin Luther King, who was then unknown. The following 10 years would see a huge, mostly non-violent struggle for African Americans' right to vote and an end to segregation.
Democrat congressman John Conyers, for whom Ms Parks worked in Detroit for 20 years, wrote the resolution. "We think having her body lie in honour in the Rotunda is probably the most expressive way that we can let everyone know the legacy of Rosa Parks is embraced by the federal legislature," he said. "I must say that the bipartisan support has been excellent."
The US senate voted on Thursday to allow the honour and the House of Representatives endorsed it yesterday. Eva Malecki, a spokeswoman for the Architect of the Capitol, said the office was already working on seating and placement of the casket.
"The movement that Rosa Parks helped launch changed not only our country but the entire world, as her actions gave hope to every individual fighting for civil and human rights. We now can honour her in a way deserving of her contributions and legacy," said senate minority leader Harry Reid, a Nevada Democrat.
Ms Parks has been the subject of numerous vigils over the last week, including a service in Martin Luther King's old church yesterday, and her body will be the focus of ceremonies in three cities. Today she will lie in state in her home, Montgomery, before being flown to Washington DC tomorrow afternoon. On Monday she will be flown to Detroit, where she moved from Alabama and where she will be buried on Tuesday. Officials expect huge crowds.
"It's easily going to be in the tens of thousands," executive assistant to the Montgomery mayor, Bobby Bright, told USA Today. In Montgomery and Detroit, bus seats were used to commemorate Ms Parks. "We cannot do enough to pay tribute to someone who has so positively impacted on the lives of millions," the mayor of Detroit, Kwame Kilpatrick, said.