The US president said trade links had been "strengthened" by the signing of the deal, which will see the terms of a similar agreement between the EU and the US continue to apply to the UK after Brexit.
He described the UK and US as having a "very good trading relationship", despite having previously warned that Theresa May's Brexit deal could harm business links.
Mr Trump was speaking after the UK government announced that it had signed a Mutual Recognition Agreement on Conformity Assessment (MRA) with the US.
The deal continues the terms of the EU-US MRA after Brexit, allowing goods made in the UK to be sold in the US, and vice versa, with less bureaucracy for manufacturers and exporters.
UK-US trade in the sectors covered by the deal is worth up to £12.8bn, the government said, including UK exports of £8.9bn, most of them in the pharmaceutical industry. Other sectors covered include tech and telecoms.
The UK has signed similar agreements with Australia and New Zealand in recent weeks as it prepares for trade outside the EU.
Speaking outside the White House, Mr Trump said: "The UK and the US are agreeing to go forward and preserve our trade agreement.
"We have a very good trading relationship with the UK and that's just been strengthened further. So with the UK we're continuing our trade and we're going to acutally be increasing it very substantially as time goes by.
"We expect that the UK will be very, very substantially increased as it relates to trade with the United States - the relationship there is very good."
Liam Fox, the international trade secretary, welcomed Mr Trump's comments.
He said: “President Trump’s statement was clear – the UK and the USA share a special trade relationship and there is real ambition on both sides of the Atlantic to enhance this after we leave the European Union. We have already taken concrete steps towards this including the signing of a Mutual Recognition Agreement earlier this week which will secure trade worth up to £12.8bn.
“A free trade agreement with the United States is one of my international economic department’s top priorities and I look forward to beginning formal negotiations.”
Earlier, announcing the deal, Mr Fox said: "The UK and the US are the strongest of trading partners and this agreement will allow British and American businesses to keep trading as freely as they do today, without additional bureaucracy."
The US is the UK's largest trading partner outside the EU, with total trade worth £184bn.
Ministers hope to agree a much more comprehensive Free Trade Agreement with the US after Brexit, although Mr Trump has previously said that this could be made more difficult by Ms May's proposed withdrawal agreement.
Speaking shortly after the deal was agreed last November, he said: "Sounds like a great deal for the EU.
“I think we have to look seriously at whether or not the UK is allowed to trade because you know right now, if you look at the deal, they may not be able to trade with us.
"That wouldn't be a good thing. I don't think they meant that, I don't think the prime minister meant that and hopefully she'll be able to do something about that but right now as the deal stands they may not be able to trade with the US and I don't think they want that at all, that would be a very big negative for the deal.”
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