The two countries will begin negotiations next year to expand their commercial agreements to cover digital trade, the environment and women's economic empowerment, the U.K.'s Department for International Trade said in an emailed statement on Saturday.
Taoiseach Micheál Martin has said he hopes the outline of a Brexit free trade deal will have emerged by the end of the week.
Announcing the deal, Prime Minister Boris Johnson said: "This is a fantastic agreement for Britain which secures transatlantic trade with one of our closest allies".
No new trade deals can start until the transition period ends on 31 December. The U.K.is Canada's third-largest export market after the US and China.
"Time is short. Fundamental divergences still remain, but we are continuing to work hard for a deal", Barnier said on Twitter. "We look forward to striking a new more ambitious deal next year with the aim of creating more opportunities for businesses and improving the lives of people across the country".
It comes as Bank of England governor Andrew Bailey has said that a no-deal Brexit would cause even more long-term damage to the UK's economy than the coronavirus pandemic.
The document will pave the way for negotiations for a new, adapted agreement from 2021, according to London.
The British Sun newspaper reported that the negotiators were looking at a clause that would allow a renegotiation of any new fishing arrangement in several years.
There is a small outpost of British territory in the Pacific Ocean in the form of the Pitcairn Islands.
The prime minister previously joked an agreement between the United Kingdom and Australia would see an exchange of chocolate biscuits in the form of British Penguins and Australian Tim Tams.
Mr Johnson's comments come after Britain and Canada agreed to continue trading under the same terms as the current European Union deal after the Brexit transition period ends at the close of the year. Officials said this shouldn't scupper an eventual deal on the future trading and security relationship, and both sides are now upbeat about their chances of success.
"I think it's in the best interests of both sides for there to be a trade agreement and for that trade agreement to have a strong element of goodwill around it on how it's implemented", he told British lawmakers on the Treasury Select Committee.