Mr Obama said Washington's current approach was "outdated" and the changes were the "most significant" in US policy towards Cuba in 50 years.
Cuban President Raul Castro said he welcomed the shift in a TV address.
The move includes the release of US contractor Alan Gross and three Cubans held in the US.
Wednesday's announcements follow more than a year of secret talks in Canada and at the Vatican, directly involving Pope Francis.
US-Cuba relations have remained frozen since the early 1960s, when the US broke off diplomatic relations and imposed a trade embargo after Cuba's revolution led to communism.
'Respectful'The US is looking to open an embassy in Havana in the coming months, Mr Obama said on Wednesday.Mr Obama and Mr Castro met a year ago at Nelson Mandela's funeralThe plans set out in a White House statement also include:
Reviewing the designation of Cuba as a state sponsor of terrorismEasing a travel ban for US citizensEasing financial restrictionsIncreasing telecommunications linksEfforts to lift the 54-year-old trade embargoMr Castro said the changes were something Cuba had been pressing for for a long time.
"Ever since my election… I have reiterated on many occasions our preparedness to hold a respectful dialogue with the government of the United States based on sovereign equality," he said.President Castro urged Washington to lift a trade and economic embargo imposed on the communist-run island – a move that can only be made by Congress.
Republican Senator Marco Rubio has criticised the new US policy, saying it would do nothing to address the issues of Cuba's political system and human rights record.
Full article on BBC news site Reported 17 December 2014