Mr Johnson has said he "strongly disagrees" with the court ruling but that Parliament "will come back".
Speaking in New York, the Prime Minister said: "Obviously this is a verdict that we will respect and we respect the judicial process.
"I have to say that I strongly disagree with what the justices have found. I don't think that it's right but we will go ahead and of course Parliament will come back."
The prime minister is expected to fly home overnight on Tuesday, a few hours earlier than planned, so that he can be in Parliament on Wednesday, ITV News Political Editor Robert Peston said.
He called the judgement "unusual" as prorogation had been used before and "had not been contested in this way."
The PM spoke to the Queen following the Supreme Court ruling, according to a senior Government official.
The official described the discussion as having taken place "earlier on today" and having been "after the verdict".
But the official would not comment on whether Boris Johnson apologised to the Queen.
"We never in any circumstances discuss the contents of conversations between the Prime Minister and her majesty," the official said.
Mr Johnson also held a telephone call with his full Cabinet lasting for about 30 minutes to update them on the ruling, expressing that he disagrees with the decision but that he respects the independence of the judiciary.
A batch of MPs have also announced they will returning to Parliament tomorrow, including Labour MPs Rose Duffield, Anna McMorrin and Tracy Brabin.
But Mr Johnson continued to say he will get on and deliver Brexit by October 31, despite MPs ruling the UK is unable to leave the EU without a deal.
The prime minister met business leaders at the UN General Assembly, before meeting President Donald Trump.
During a UN meeting with President Trump, Mr Johnson appeared to rule out resigning over the Supreme Court result.
After the PM was questioned about stepping down, Mr Trump said: "I'll tell you, I know him well, he's not going anywhere."
Mr Johnson added: "No, no, no."
The panel of 11 justices at the Supreme Court agreed unanimously on Tuesday the prorogation of parliament had the effect of frustrating the House of Commons.
The court also found the suspension was "void and of no effect" - meaning Parliament has not been suspended.
Labour leader Jeremy Corbyn called for Mr Johnson to resign following the Supreme Court decision, with supporters chanting "Johnson out."
Opening his speech to his party's annual conference in Brighton, Mr Corbyn said: "The Government will be held to account for what it has done. Boris Johnson has been found to have misled the country.
"This unelected prime minister should now resign."
Mr Corbyn said Boris Johnson would become "the shortest-serving prime minister in history" if he stood down.
The Labour leader has called for a general election in the wake of the Supreme Court ruling, but won’t vote for one until a Brexit delay is guaranteed.
The advice of Attorney General has been called into question and whether he gave legal advice to Mr Johnson that prorogation was 'lawful'.
A spokeswoman from the Attorney General's Office said: "The Government acted in good faith and in the belief that its approach was both lawful and constitutional.
"These are complex matters on which senior and distinguished lawyers have disagreed."
Commons speaker John Bercow welcomed the Supreme Court decision and said the Commons "must convene without delay."
He has instructed the House of Commons to return on Wednesday from 11.30am, following the Supreme Court decision.
Speaking to reporters, he said: "That judgement is unanimous, that judgement is unambiguous, and that judgement is unqualified."
In a statement, he said: "In reaching their conclusion, they [judges] have vindicated the right and duty of Parliament to meet at this crucial time to scrutinise the executive and hold Ministers to account."
The Supreme Court's president Lady Hale said the issue of suspending Parliament was "justiciable" - capable of challenge in the courts.
She added this was not a normal prorogation and the speakers of the Houses of Commons and Lords "can take immediate steps to enable each house to meet as soon as possible".
Announcing the result, Lady Hale said: "The court is bound to conclude, therefore, that the decision to advise Her Majesty to prorogue Parliament was unlawful because it had the effect of frustrating or preventing the ability of Parliament to carry out its constitutional functions without reasonable justification."
She added the suspension of parliament took place in "exceptional circumstances" and said the case is a "one-off", having come about "in circumstances which have never arisen before and are unlikely to ever arise again."
The Supreme Court's decision came after two other legal rulings on the suspension came to separate decisions.
At the High Court in London, judges rejected a challenge against the prime minister's prorogation move by campaigner and businesswoman Gina Miller.
But in Scotland, a cross-party group of MPs and peers won a ruling from the Inner House of the Court of Session that Mr Johnson's prorogation decision was unlawful because it was "motivated by the improper purpose of stymieing Parliament".
Reacting to the court's decision, Ms Miller said: "Today's ruling confirms that we are a nation governed by the rule of law. Laws that everyone, even the Prime Minister is not above.
"Do not let the government play down the seriousness of the judgement today."
Joanna Cherry QC, an SNP MP who helped bring the case against the prorogation of parliament to the Supreme Court, said there was "nothing" stopping parliament from re-convening.
She said: "His position is untenable and he should have the guts, for once, to do the decent thing and resign."
Ian Blackford, the SNP's leader in Westminster, told reporters outside the Supreme Court: "This is a marvellous day for democracy. This is a very clear indication to Boris Johnson that you cannot shut down parliament with impunity."
He added: "We must be back in parliament immediately. I know the speaker will be consulting all party leaders. We want to get back to work.
"Quite frankly, on the back of this, Boris Johnson must resign immediately."
Former prime minister Sir John Major, who backed Ms Miller's legal campaign, said: "I hope this ruling from the Supreme Court will deter any future Prime Minister from attempting to shut down Parliament".
He added: "No Prime Minister must ever treat the monarch or Parliament in this way again".
Conservative MP Amber Rudd, who quit Boris Johnson's Cabinet and surrendered the whip earlier this month over the Government's handling of Brexit, described the Supreme Court's findings as "astonishing".
While Brexit Party leader Nigel Farage called for the prime minister's chief adviser Dominic Cummings to be sacked, adding: "The calling of a Queen's Speech and prorogation is the worst political decision ever."
Liberal Democrat leader Jo Swinson said: "The court have found what we all knew all along, Boris Johnson has again proven he is not fit to be Prime Minister.
"This shutdown was an unlawful act designed to stop Parliament doing its job and holding the Government to account."
Guy Verhofstadt, the EU's Brexit coordinator, tweeted the "rule of law in the UK is alive and kicking."
While London mayor Sadiq Khan said Mr Johnson "misled the British public, Parliament, the Queen and the Courts" about the reason he prorogued Parliament.
Former Green Party leader Caroline Lucas called for Britain to have a written constitution.
"Thankfully the Supreme Court has ruled unanimously in our favour, but it should never have come to this," the Brighton Pavilion MP said.
"It shouldn't require the courts that have to uphold parliamentary sovereignty."
Mr Johnson claimed the five-week suspension was to allow the Government to set out a new legislative agenda in a Queen's Speech when MPs return to Parliament.
But those who brought the legal challenges argued the prorogation was designed to prevent parliamentary scrutiny of the UK's impending exit from the EU on October 31