Parks, who died Monday in Detroit at age 92, also will be the first woman to lie in honor in the Rotunda, the vast circular room under the Capitol dome.
The House on Friday passed by voice vote a resolution allowing Parks to be honored in the Capitol on Sunday and Monday "so that the citizens of the United States may pay their last respects to this great American." The Senate approved the resolution Thursday night.
The viewing will extend from 6 p.m. Sunday afternoon until midnight and also run from 7 a.m. until 10 a.m. Monday.
It will be only the fifth time in the past two decades that a person has either laid in honor or in state in the Rotunda. The last to lie in state was President Ronald Reagan after his death in June last year.
The refusal by Parks, a black woman, to give up her bus seat to a white man in then-segregated Montgomery, Alabama, in 1955 led to a 381-day boycott of the city's bus system and helped ignite the modern civil rights movement.
"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," said Senate Democratic leader Harry Reid. "We now can honor her in a way deserving of her contributions and legacy."
In most cases, only presidents, members of Congress and military commanders have been allowed to lie in the Rotunda.
Parks would be the first woman and second black American to receive the accolade. Jacob J. Chestnut, one of two Capitol police officers fatally shot in 1998, was the first black American to lie in honor, said Senate historian Richard Baker.
Parks also would be the second non-governmental official to be commemorated that way. The remains of Pierre L'Enfant — the French-born architect who was responsible for the design of Washington, D.C. — stopped at the Capitol in 1909, long after his death in 1825.
"Rosa Parks is not just a national hero, she is the embodiment of our social and human conscience and the spark that lit the flame of liberty and equality for African Americans and minority groups in this country and around the globe," said Sen. Christopher Dodd, a Democrat.
Officials with the Rosa & Raymond Parks Institute for Self Development in Detroit said at one point that Parks would lie in repose at the Lincoln Memorial. The National Park Service, however, said those plans were never formalized.