The deal is believed to be worth about $890 million.
The move has sparked outrage and confusion among pro-Brexiteers, with former Cabinet minister Priti Patel slamming the move as "a disgraceful decision" and "perverse".
"This should be a moment that we should be celebrating. The return of our iconic blue passport will re-establish the British identity," she said, adding: "It is a national humiliation."
She joined a chorus of voices urging the government to reconsider the deal.
"I am very sorry to hear it, as De La Rue has a factory in my constituency," Conservative MP Jacob Rees-Mogg said.
"It seems odd to have a national symbol produced abroad."
When it submitted its bid to renew its passport contract in November, De La Rue's chief executive Martin Sutherland said it would be "a shame" if the British company did not continue making the national travel document.
"It would be a shame if in the year of Brexit the contract was lost and the British passport was not printed by a British company," he said.
Government ministers were not allowed to know who had submitted bids under the "blind tender" process and civil service procurement rules prohibited the government from discriminating against the bids of EU nations.
The Sun reported that the bidding companies could mount legal challenges to the decision.
It also said Gemalto was likely to make the bodies of the travel document abroad but all security aspects, such as data chips, must be made in the UK.
A spokeswoman for the Home Office told The Sun that British passports did not have to be made in the UK.
"We are running a fair and open competition to ensure that the new contract delivers a high quality and secure product and offers the best value for money for customers," the spokeswoman said.
"All passports will continue to be personalised with the holder's details in the United Kingdom, meaning that no personal data will leave the UK.
"We do not require passports to be manufactured from the UK. A proportion of blank passport books are currently manufactured overseas, and there are no security or operational reasons why this would not continue."
Burgundy was adopted as the colour of the UK passport in 1988 and a replaced a dark shade of blue — which some people argued was black — that had been used since 1920.
Prime Minister Theresa May said in December the UK passport would revert back to "iconic" blue in line with its exit from the European Union.
"The UK passport is an expression of our independence and sovereignty — symbolising our citizenship of a proud, great nation," Ms May tweeted at the time.
"That's why we have announced that the iconic blue passport will return after we leave the European Union in 2019."
The new passports will be introduced after the UK leaves the bloc in March 2019.