With just five months until Britain leaves the European Union, its biggest foreign policy shift in more than 40 years, Hunt said Britain plans to hire nearly 1,000 more diplomatic staff, open new embassies and boost language training.
"This country is at a pivotal historic moment, the global balance of power is shifting once more and post-Brexit our place within it changes as well," Hunt said in a speech at the Policy Exchange think tank.
"At the same time our democratic values are arguably under greater threat than at any time since the fall of the Berlin Wall ... we can use our influence, our reach and power to defend our values by becoming an invisible chain that links the world's democracies."
Since Britain voted in a 2016 referendum to leave the EU, the government has repeatedly flagged its ambition for a 'Global Britain', but lawmakers and foreign policy experts have accused it of lacking a strategy or resources to deliver on that goal.
Hunt said Britain needed to redouble its efforts to defend the international rules-based order and support reform of international institutions including the United Nations, the World Trade Organization, the World Bank and the Commonwealth.
The Foreign Office has faced budget cuts under successive governments which have seen it reduce embassy jobs and sell off exotic properties overseas. At the same time its remit has shrunk, with key policy areas including foreign aid, trade and the relationship with the EU moved to other departments.
The Foreign Office's operating expenditure fell by 21.6 percent between 2010 and 2015 and was then frozen in real terms, spending watchdog the National Audit Office said last year.
"There is a mismatch between the rhetoric and ambition around a Global Britain and actually what we invest in the diplomatic service itself," said Tom Raines, head of the Europe Programme at global affairs think-tank Chatham House.
The mismatch, he added, was "quite obvious to others".
In his speech, entitled "Britain's role in the world after Brexit", Hunt said the new jobs would be in place by the end of 2020 and would include 335 diplomatic positions overseas, 328 in London and 329 new local staff around the world.
According to the National Audit Office, the Foreign Office employed 12,865 staff globally in 2016-17.
"We have to reinvigorate and expand British diplomacy. In the past you may have heard of retrenchment and retreat, not anymore," Hunt said, adding that he would also open up "one or two" ambassador posts a year to those outside the civil service, particularly business people.
The government said it would create 12 new embassies or missions, many of them in Commonwealth countries as it looks to revitalise links with former colonies.
The Foreign Office also plans to boost language training, doubling the number of diplomats who speak the local language and increasing the number of languages taught at the department to 70 from 50, including the addition of Kazakh and Gujarati.
"There is a perception in many places that Brexit is an isolationist or backwards step for the UK, which has generally been seen as internationalist and open... so there is a big job for the UK to correct that narrative," said Raines. (Additional reporting by David Milliken; editing by Stephen Addison and Gareth Jones)
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