Mr Hammond's arrival makes him the first UK foreign secretary to visit since the years before the Caribbean country's communist revolution of 1959.
He said the UK was set to reach new "co-operation agreements" on energy, education and culture with Cuba.
Mr Hammond's visit follows one by US President Barack Obama last month.
The foreign secretary is due to take part in a series of meetings to discuss social and economic changes, human rights and the fight against global health threats such as the Zika virus.
He will also sign a bilateral agreement restructuring Cuba's debt to the UK.
"Britain and Cuba have outlooks on the world and systems of government that are very different," Mr Hammond said as he arrived in the capital Havana.
"But as Cuba enters a period of significant social and economic change, I am looking forward to demonstrating to the Cuban government and people that the UK is keen to forge new links across the Atlantic.
"That is why Cuba and the UK are set to reach new cooperation agreements on energy, financial services, education and culture, to the benefit of both our nations.
"As the first British foreign secretary to visit Cuba since before the Cuban Revolution in 1959, this is an opportunity to hear for myself what Cuba thinks about its present challenges and where it sees its future."
Last year, British exports to Cuba soared by 25%. According to the Department of Trade and Industry, the top items exported to the country are:
In March Barack Obama became the first US president since 1928 to visit Cuba.
For years, the US and Cuba were engaged in a bitter stand-off, triggered by the overthrow of US-backed Cuban dictator Fulgencio Batista by Communist leader Fidel Castro in 1959.
The US broke off diplomatic relations and imposed a trade embargo.

Arriva Rail North staff will walk out for three days from 8 July, while Merseyrail staff will strike on 8, 10 and 23 July, the final day of The Open.
Workers at Southern also plan to walk out on 10 July.
The RMT is in dispute with the rail companies over driver-only-operated trains which they say would be unsafe and lead to widespread job losses.
The strike will also clash with the British Style Collective, the Clothes Show's big event in Liverpool from 7 - 9 July.
RMT General Secretary Mick Cash said any responsibility for disruption to services lay with the companies and their refusal to enter meaningful talks with the union.
"It is that flagrant disregard for the safety issues at the heart of the dispute which leaves us with no option but to press on with the campaign of strike action," he added.
However, Richard Allen, deputy managing director for Arriva-run Northern, said he was "deeply disappointed and hugely frustrated" by the announcement of further action.
"Only this week we wrote to RMT again, urging them to engage in meaningful modernisation talks with us.
"We have been clear that for all our conductors we are prepared to guarantee jobs and current pay, and continue with annual pay reviews, if we can reach agreement with RMT," Mr Allen said.
He added fresh industrial action would not solve the dispute.
Merseyrail's managing director Jan Chaudhry-van der Velde criticised the timing of the strike which he said was designed to "cause maximum disruption to people attending the last day of the Open Golf at Royal Birkdale".
Mr van der Velde claimed the company "brought several new initiatives to the table in the last round of talks, the RMT is unprepared to work with us to find middle ground".
"While we, as always, will do our best to minimise disruption, our passengers should not be made to suffer at the hands of the RMT, and the Liverpool City Region should not be caught in the cross-fire of a national dispute directed by unions in London."
The latest strike announcement comes as a long-awaited report into the troubled Southern rail franchise has blamed the unions for widespread disruption over the last year.
Foreign Secretary Philip Hammond said he was keen to "forge new links across the Atlantic" as he arrived in Cuba for a historic visit.
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Train passengers across England are to be hit by further strike action, RMT officials have said.