David Davis says the UK can negotiate a "bespoke" trade deal with the EU more wide-ranging than the one with Canada within less than a year.
The EU's deal with Canada, which came into force in September, took seven years to negotiate. But it does not extend to services - which make up 80% of Britain's economy and include the crucial financial sector.
In his first TV interview since Theresa May struck a deal with Brussels on the divorce issues in the early hours of Friday, the Brexit Secretary claimed striking a free trade deal with arrangements for specific sectors "is not that complicated".
Trade talks with the EU are set to begin next year following Theresa May's last-minute breakthrough on the divorce issues of money, EU citizens and the Northern Irish border.
Mr Davis told the BBC's Andrew Marr Show that Britain could have a better deal than those the EU has signed with other third countries in recent years.
"What we want is a bespoke outcome," he said. "We'll probably start with the best of Canada, and the best of Japan and the best of South Korea and then add to that the bit that's missing, which is the services.
Mr Davis said he aimed to negotiate "individual specific arrangements for aviation, for nuclear for data - a whole series of strange which we've worked out". He added: "'Canada plus plus plus' would be one way of putting it."
Asked whether it was realistic to strike such a deal within eight months, as it is expected the outlines of such a deal would need to be presented to the EU27 next October, he claimed it could be signed "minutes" after Britain's official departure date at the end of March 2019.
"It's not that complicated," Mr Davis said, pointing out that Britain's regulations and standards are already aligned with the EU.
He also insisted that Britain would not pay a divorce bill of £39bn unless a trade agreement is reached after a two-year transition period, in an attempt to quell discontent among Tory MPs.
Tory Brexiteer Peter Bone later told Sky News of the deal between Brussels and London: "Am I unhappy with bits of it? Absolutely! the £39 billion we suddenly found. That is actually more than £350m a week and I think we said we might spend on the NHS."
Mrs May is poised for Cabinet tensions between her Brexiteers and former Remain supporters to be aired next week, when her top team discusses the shape of a future trade deal for the first time.