Boris Johnson should resign after the Supreme Court found his suspension of Parliament is unlawful, First Minister Mark Drakeford has said.
The court's justices found that, in effect, the five-week prorogation never took place.
It is a "victory for the rule of law", Mr Drakeford said.
But Brexiteers called for a general election, with Monmouth MP David Davies saying the prime minister was facing a "pro-EU establishment".
House of Commons Speaker John Bercow has said Parliament will resume at 11:30 BST on Wednesday.
Downing Street said it was "currently processing the verdict".
Mr Drakeford said: "The prime minister tried to play fast and loose with our constitution. The unanimous decision by the Supreme Court is a huge victory for the rule of law.
"Parliament was never prorogued and must now hold this government to account."
He tweeted: "Any normal prime minister would - as a matter of honour - tender their resignation after such a unanimous verdict from the UK's highest court.
"It is the final straw in a pitiful episode for the country."
Prime Minister Boris Johnson controversially announced on 28 August that Parliament would be suspended until mid-October, causing a row with opposition politicians.
The Welsh Government argued it got in the way of the work of the assembly - opposition MPs complained it meant they were unable to properly scrutinise the UK government ahead of Brexit.
Ruling unanimously, the Supreme Court's 11 judges found the PM's advice to the Queen was "unlawful, void and of no effect" when he asked the Queen to suspend Parliament.
The decision "had the effect of frustrating or preventing" parliament from carrying out its functions, it said.
The Supreme Court made its judgement following cases in the English and Scottish courts, the former backed by the Welsh Government, the latter supported by a number of Welsh MPs.
They included Jo Stevens, Cardiff Central Labour MP, who said: "That was a comprehensive demolition by the Supreme Court of the liar we unfortunately have as Prime Minister. He must resign."
Labour's MP for Cardiff South and Penarth Stephen Doughty told the BBC: "He's lied to the Queen, he's acted unlawfully and he's played fast and loose with our constitution and our basic principles.
"The Supreme Court unanimously is upholding our constitution. What he's done is he prevented us as members of Parliament from not only doing our job on Brexit but on so many other issues, from pensions to climate change to health to education."
Plaid Cymru MPs also backed the Scottish case. Party leader Adam Price said: "There is only one response now acceptable by the prime minister to this damning and unanimous judgement by the Supreme Court: Resign."
"After getting rid of this dishonest prime minister Parliament must now move to end the chaos and uncertainty and take it back to the people in a People's Vote so we can finally move on from this dark chapter in our politics."
Westminster Plaid leader Liz Saville Roberts said: "The prime minister has shown himself to be no better than a tin-pot dictator, shutting down democracy to avoid scrutiny."
Some MPs, including Swansea East MP Carolyn Harris, tweeted pictures of themselves returning to the green benches. The House of Commons speaker John Bercow has said he is consulting party leaders.
He said Parliament "must convene without delay".
Welsh Liberal Democrat leader Jane Dodds welcomed the "damning judgement from the courts that confirms the prorogation of Parliament was unlawful and politically motivated".
"Parliament must be recalled now so we can get on with our jobs," she said. "With the Brexit clock still ticking down there isn't a moment to lose."
Monmouth Conservative MP David Davies defended the Tory leader, saying he stood with Mr Johnson "who is doing everything possible to deliver on the clear result of a referendum in the face of a powerful pro EU establishment".
"They want the PM to resign - but they don't want an election," he said.
He added: "The PM has given opposition parties two chances for an election.... we should offer a third."
Former Welsh Conservative assembly group leader Andrew Davies called for an election.
"The courts have had their say, Parliament has had its say, now it's time the people had theirs," he said.
Analysis by James Williams, BBC Wales political correspondent
Boom! The Supreme Court has just dropped a political bombshell that could well blow up Boris Johnson's premiership.
His political opponents have been lobbing their own grenades in to the mix as the calls for him to resign come thick and fast.
But it's how his own Conservative troops respond that's likely to determine whether the prime minister can continue to bunker down in Downing Street.
Number 10 says it is "currently processing the verdict".
However, if his own side turns on him after this extraordinary verdict, then Boris Johnson's next move may well be determined for him.
On Monday, Mr Johnson refused to rule out suspending Parliament for a second time if the Supreme Court ruled against him.
Former First Minister Carwyn Jones said that would put the Queen in an "invidious position".
Following the ruling, he told BBC Wales: "If you were the Palace, you would be saying: Having been told that the advice was improper, how can we sure that the advice is proper this time round?
That would put the Queen in an invidious position of having to agree to something potentially on the basis of advice that's actually in effect illegal."