In posts on Truth Social, Trump said he would hold an Oval Office news conference on Thursday morning about a "full and comprehensive" trade agreement with Britain.
Prime Minister Keir Starmer, who describes the US as an indispensable ally, is due to provide an update later on Thursday.
The deal is likely to be narrow, with Britain securing lower tariffs on cars and steel, the two sectors hardest hit.
"Because of our long time history and allegiance together, it is a great honor to have the United Kingdom as our FIRST announcement," Trump said.
"Many other deals, which are in serious stages of negotiation, to follow!"
The United States has been under pressure from investors to strike deals to de-escalate its tariff war after Trump's often chaotic policymaking upended global trade with friends and foe alike, threatening to stoke inflation and start a recession.
Top US officials have engaged in a flurry of meetings with trading partners since the president on April 2 imposed a 10 per cent tariff on most countries, along with higher tariff rates for many trading partners that were then suspended for 90 days.
The US has also imposed 25 per cent tariffs on autos, steel and aluminium, 25 per cent tariffs on Canada and Mexico, and 145 per cent tariffs on China.
US and Chinese officials are also preparing to hold talks in Switzerland on Saturday, which could mark the first step in resolving a potentially damaging trade war between the world's top two economies.
Britain was not among the countries hit with additional tariffs because it imports more from the US than it exports there.
Starmer, who has struggled in government since he was elected last July with his centre-left Labour Party, has struck up a warm relationship with Trump and his government will celebrate becoming the first country to agree on a deal.
A British official had said that the scope of any agreement was likely to be narrow, with Britain expected to secure lower tariffs on a tranche of steel and autos exports.
In return, Britain is likely to agree to lower its own tariffs on US cars and cut a digital sales tax that affects US tech giants.
It had refused to lower its food standards, which are closely aligned with the European Union.
However, Britain's farming trade union has said that some US producers do meet British standards by not using growth hormones or antimicrobial washes, and could be given greater market access.
Starmer's government has been walking a tightrope on trade, seeking as an independent country after Brexit to build new ties with the US, China and the EU without moving so far towards one bloc that it angers the others.
There are also political threats on the domestic front.
Polling shows the government remains deeply unpopular after it cut support for pensioner's energy bills and hiked taxes on households and companies.
Investors have been looking to see whether Trump can de-escalate his trade war after the launch of global tariffs risked reigniting inflation and slowing economic growth.
For Britain, the government is trying to reduce the worst of the damage from Trump's tariffs without damaging its efforts to reset its trade relationship with the European Union.
It also agreed a new trade deal with India earlier this week.
