A clock counting down to the moment Britain leaves the EU, at 11pm on 31 January, will be projected onto the outside of No 10, it was announced.
The package appeared to have been rushed out to try to calm protests from hardline Brexit supporters over the fiasco of the silencing of the world’s most famous clock.
Mr Johnson has been criticised after his proposal of crowdfunding the £500,000 bill for restoring Big Ben to working order for Brexit day backfired badly.
Supporters have raised more than £200,000 in just three days, but the plan has been stamped on by the parliamentary authorities who said they would not accept publicly raised money.
No 10 is now seeking to distance itself from the campaign, insisting it is a matter for MPs, despite the prime minister proposing it in the first place.
Downing Street declined to put a cost on its celebrations, but said they were intended to “heal divisions, re-unite communities and look forward”.
It is expected that broadcasters will be asked to replicate the sound of Big Ben ringing out to make up for the absence of the real thing.
Mr Johnson will be one of the first people to receive one of the newly-minted 50p pieces after the first batch had to be melted down when Brexit was delayed in October.
A special meeting of the Cabinet will be staged somewhere in the north of England on 31 January to emphasise the government’s pledge to “level up” the country.
Meanwhile, Brexiteers continued to rage over the Big Ben fiasco, with Tory MP Mark Francois revealing he had donated £1,000.
“We are now not far short of £220,000 and, by the end of the day, we probably won’t be a million miles away from having raised half the total in two days,” he said.
Former Tory leader Iain Duncan Smith insisted Big Ben rings on all the “big occasions”.
“It sounded out the end of the war in Europe, it sounded out the end of the war in Japan, and when we joined the EU,” he said.
“And as we leave – arguably the biggest decision we have made since the end of the war – then the bell, I think, should sound for that.”
Meanwhile, the European Parliament confirmed that the Union flag which flies above the building in Strasbourg will be lowered after Britain’s exit and sent to the House of European History.