The new department is opening after No 10 decided to combine the Foreign and Commonwealth Office with the Department for International Development (DfID).
Critics have said the move could weaken British influence and reduce expertise.
But the government said it would allow the country to be "a force for good".
In a statement announcing the launch of the department, the government also said it had "committed to spending 0.7% of our national income on aid" - despite renewed pressure from some in the Conservative Party over the weekend to scrap the target.
To mark its first day in business, the department's lead minister, Foreign Secretary Dominic Raab, announced a £119m fund to tackle coronavirus and famine.
The money will be targeted in Yemen, the Democratic Republic of Congo (DRC), Somalia, Central African Republic, South Sudan, Sudan and West Africa's Sahel region - all places where the outbreak has worsened conditions for people already struggling with extreme hunger, wars and/or climate change.
Mr Raab said: "Coronavirus and famine threaten millions in some of the world's poorest countries, and give rise to direct problems that affect the UK, including terrorism and migration flows.
"Global Britain, as a force for good in the world, is leading by example and bringing the international community together to tackle these deadly threats, because it's the right thing to do and it protects British interests."
The foreign secretary also confirmed he would be appointing Nick Dyer - a director general at DfID - as the UK's first special envoy for famine prevention and humanitarian affairs.
The abolition of the Department for International Development may have been driven by political pressure from within the Conservative Party.
But the government argues that its merger with the Foreign Office will mean better, more joined-up policy.
Foreign Secretary Dominic Raab said that by combining its diplomatic strength with its expertise in foreign aid, Britain could not only tackle global challenges, but also protect its interests.
Critics fear the new Foreign Commonwealth and Development Office could mean the government weakens its commitment to spend 0.7% of national income on foreign aid.
But Downing Street insisted there'd been no change to that policy.
The two departments have a history of being merged and split up again, and the move to bring them together has long been mooted in Conservative circles.
Boris Johnson announced the merger in June, telling MPs it would ensure aid spending better reflected UK aims and that it was a "long overdue reform".
He said UK aid spending had "been treated as some giant cashpoint in the sky that arrives without any reference to UK interests".
But the PM pledged DfID's budget - which at £15bn last year dwarfed the £2.4bn spent by the Foreign Office - would be maintained
Mr Johnson's decision was criticised by three previous prime ministers - Conservative David Cameron, and Labour's Gordon Brown and Tony Blair.
Mr Cameron said it would mean "less expertise, less voice for development at the top table and ultimately less respect for the UK overseas".
The Commons International Development Committee also called the move "impulsive", saying the world's poorest "will pay the greatest price".
Labour leader Sir Keir Starmer pledged to reinstate DfID if he were to win the next general election, saying the merger was "the tactics of pure distraction".