Land Of Hope And Glory and Rule Britannia! will be performed at the Last Night Of The Proms, the BBC has said.
The confirmation comes after The Sunday Times said organisers feared a backlash because of the perceived association the traditional anthems have with colonialism and slavery.
Downing Street waded into the controversy and Culture Secretary Oliver Dowden said he had written to the BBC over the issue.
A statement from the BBC on Monday evening said: "With much reduced musical forces and no live audience, the Proms will curate a concert that includes familiar, patriotic elements such as Jerusalem and the national anthem, and bring in new moments capturing the mood of this unique time, including You'll Never Walk Alone, presenting a poignant and inclusive event for 2020."
Dalia Stasevska, from Finland, is conducting the Last Night this year, with soprano Golda Schultz and the BBC Symphony Orchestra performing.
The corporation's statement said: "We very much regret the unjustified personal attacks on Dalia Stasevska, BBC Symphony Orchestra principal guest conductor, made on social media and elsewhere.
"As ever, decisions about the Proms are made by the BBC, in consultation with all artists involved."
The BBC said a new arrangement of Jerusalem will be performed, along with orchestral versions of Land Of Hope And Glory and Rule Britannia!.
In the statement, the broadcaster said: "The programme will include a new arrangement by Errollyn Wallen of Hubert Parry's Jerusalem alongside new orchestral versions of Pomp And Circumstance March No. 1 'Land Of Hope And Glory' (arr. Anne Dudley) and Rule Britannia! as part of the Sea Songs, as Henry Wood did in 1905."
Earlier, a Number 10 spokesman said the Prime Minister believes in tackling the "substance" not the "symbols" of problems.
"This is a decision and a matter for the organisers of the Proms and the BBC," the spokesman said.
"But the PM previously has set out his position on like issues and has been clear that while he understands the strong emotions involved in these discussions, we need to tackle the substance of problems, not the symbols."
Culture Secretary Mr Dowden said that "confident, forward-looking nations don't erase their history".
He wrote on Twitter: "Rule Britannia! and Land of Hope and Glory are highlights of the Last Night of the Proms.
"(I) Share concerns of many about their potential removal and have raised this with (the) BBC.
"Confident forward-looking nations don't erase their history, they add to it."