Referring to a decade-long campaign that began in 1996 in which more than 13,000 people died, Prachanda, the leader of the Maoists, said: "This is an epoch-making day, a historic day that is at the height of the years of struggle by the Nepalese people since the 1950s.
"It has come after struggle and sacrifice by thousands of martyrs."
Abolishing the 239-year-old monarchy was a key part of the peace deal with former Maoist fighters, who emerged as the largest party in elections to the 601-member assembly in April.
|Gyanendra could be forced to vacate his palace|
in Kathmandu if he refuses to leave [AFP]
Police are out in the streets of Kathmandu to maintain order.
The city is tense after at least three bomb blasts in the past couple of days, some blamed on pro-royalist groups. No one was killed in the explosions.
The government has banned rallies near the assembly venue and other royal sites, but thousands of anti-monarchists say they will take to the streets to celebrate anyway.
The government said on Tuesday that it could use force to throw Gyanendra out of the palace if he refuses to leave.
"The king must leave the palace immediately and move to the Nirmal Niwas," Ram Chandra Poudel, peace and reconstruction minister, said, referring to Gyanendra's private home.
"If he does not leave the palace then the government might have to use force to [make him] vacate the palace. This will not be good for him."
Nepal's kings are believed by many of its people to be reincarnated gods.
But Nepalis say much of the mystique of the royal family was broken after the 2001 palace massacre in which Birendra, the popular king, and eight other royals were killed by then Crown Prince Dipendra, who later turned the gun on himself.
That image was further tarnished after Gyanendra fired the government and assumed absolute powers in 2005, only to be humbled by weeks of anti-king protests a year later.
King Gyanendra, widely viewed as unpopular, is expected to vacate his palace in the capital Kathmandu soon after the vote, although he has made no comment on his plans.
Already his face has been erased from Nepal's currency, and his portraits removed from the walls.
All state allowances and benefits for Gyanendra will be stopped from Wednesday.
Lok Raj Baral of the Nepal Centre for Contemporary Studies said: "This is the demand of the time and we have to move according to that demand.
"That is why I think even if we will have a worse, very turbulent phase, we have no other option but to go through it."