Prime Minister Theresa May announced the state visit during talks with Trump at the White House on Friday.
With Prime Minister Theresa May under growing pressure over her ties to Trump, opposition MPs and members of her own Conservative party have also urged ministers to reconsider the visit later this year, which would see Trump honoured by parliament and Queen Elizabeth II.
But a Downing Street spokeswoman said: "We've extended the invitation. It's been accepted."
May announced the state visit during talks with Trump at the White House on Friday, intended to reaffirm the "special relationship" and boost trade ties after Britain leaves the European Union.
But her closeness to the erratic billionaire drew fire at home, particularly when she initially failed to condemn his ban on refugees and citizens from seven mainly Muslim countries.
A petition calling for the state visit to be cancelled because his "well-documented misogyny and vulgarity disqualifies him" from meeting the queen passed one million signatures on Monday morning.
Set up several months ago, the number of signatories has surged since Trump signed his executive order on Friday -- a move that triggered global protests, with more expected in Britain later Monday.
"You are not welcome here, Mr President," headlined the Daily Mirror tabloid.
Opposition Labour leader Jeremy Corbyn, the smaller Liberal Democrats and the Scottish National Party have all called for the state visit to be cancelled, as have some Tories.
"We have to question whether ... this is something that Britain should be doing for a man who has no respect for women, disdain for minorities, little value for LGBT communities, no compassion for the vulnerable and whose policies are rooted in divisive rhetoric," Conservative Muslim peer Sayeeda Warsi told BBC radio.
Conservative MP Sarah Wollaston said Trump should not be invited to address lawmakers as Barack Obama did in parliament's Westminster Hall during his state visit in 2011.
Ruth Davidson, leader of the Scottish Conservatives, said the visit could not go ahead "while a cruel and divisive policy which discriminates against citizens of the host nation is in place".
Trump on Friday signed an executive order suspending the arrival of all refugees for at least 120 days, Syrian refugees indefinitely -- and barring citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for 90 days.
May initially refused to condemn the move, but Downing Street clarified on Sunday that London did not agree with his approach.
Foreign Secretary Boris Johnson said it was "divisive and wrong to stigmatise because of nationality" -- before announcing that, after talks with the US administration, most Britons would be exempt.
Johnson was expected to be called to the House of Commons later Monday to explain the government's response.
High-profile British citizens briefly caught up in the new US rules included Somali-born double-double Olympic champion Mo Farah, who slammed a policy based on "ignorance and prejudice" that could keep him apart from his US-based family.
The Foreign Office later announced the order would only apply to individuals travelling directly to the US from one of the seven listed countries.
Iraqi-born Conservative MP Nadhim Zahawi had also revealed he was caught up in the ban.
Trump, whose mother was born in Scotland, has made clear his fondness for Britain and has said the vote to leave the European Union was a "smart" move.
The Sunday Times newspaper claimed however that he was reluctant to meet Prince Charles, the queen's son and heir, because of the royal's strong views on the dangers of climate change.