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.
Foreign Secretary Philip Hammond said he was keen to "forge new links across the Atlantic" as he arrived in Cuba for a historic visit.