The group, headed by Glasgow-born Brian Duffy, said luxury watches in particular were being snapped up by big spenders, with the average selling price rising to almost £4,000.
It is now planning to open a store in the heart of the Square Mile in London as well as continuing its push into what it sees as the underdeveloped luxury watch market in the US.
The update came as the company released annual results for what it said had been a “pivotal year”.
The company, which joined the London stock market in May, said sales in the year to 28 April jumped 22.5 per cent to £773.5m, with pre-tax profits hitting £20.1m, up 181 per cent.
Sales of luxury watches were particularly impressive, jumping 28 per cent to £631.4m, and accounting for 82 per cent of all sales.
Overall UK same-store sales were up by 10 per cent and trading in the first 11 weeks of the current financial year was described as “encouraging”.
Watches of Switzerland is the UK’s largest retailer of Rolex, Cartier, Omega, TAG Heuer and Breitling watches and has used its size to expand throughout the year.
Trading as Goldsmiths, Mappin & Webb, Watches of Switzerland and Mayors, the group spent £33.8m on expansion of its portfolio, including seven new showrooms – with new sites in New York, Las Vegas and London – and 11 refurbishments.
As well as further new stores in the UK and US, changes planned for its retail portfolio include conversion of its Watches of Switzerland branch in Glasgow to focus on the Rolex brand by early next year.
Duffy said: “Current trading remains encouraging and we are confident of meeting the expectations for the financial year ending April 2020.
“We are the UK’s leading luxury watch retailer, hold a growing position in the US market, and operate in a highly attractive market in which demand for luxury watches generally outstrips supply.
Shares in Watches of Switzerland, which listed at 270p, rose 3p yesterday to close at 293p.
Russell Pointon at Edison Group described it as a “good set” of results, adding that the group’s “predictability makes it a relatively safe place to be in the general retail sector”.
Duffy, who has said he grew up doing a “tour” of Glasgow’s housing schemes, and who studied accountancy after leaving school, worked in finance roles for organisations including Polaroid at Vale of Leven and underwear firm Playtex at Port Glasgow before joining fashion brand Ralph Lauren in 2003.
He spent nearly a decade with the business, serving as president for Europe and the Middle East, before joining Watches of Switzerland.