He is the first sitting US president to visit since the 1959 revolution, which heralded decades of hostility between the two countries.
Mr Obama said change would happen in Cuba and that Cuban President Raul Castro understood that.
The two leaders are due to meet later on Monday to talk about trade and to hold a joint news conference.
Why is the visit groundbreaking?
For a US president to touch down at Jose Marti airport in Havana and be warmly greeted by Cuban's foreign minister was until recently unthinkable.
For decades, 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.
But President Obama undertook two years of secret talks which led to the announcement in December 2014 that the two countries would restore diplomatic relations.
Since then, there have been a series of symbolic moments, such as the first formal meeting of Presidents Obama and Castro at a regional summit in Panama and the opening of embassies in Havana and Washington DC.
What have been the highlights of the visit so far?
The first stop on President Obama's tour was the newly re-opened US embassy in Havana, where he told staff it was "wonderful to be here".
But it was the visit to Havana's old town which brought home the long way US-Cuban relations have come since the thaw was announced 15 months ago.
While the plan to interact with Cubans in the streets was disrupted by a tropical storm, the image of the US president and his family braving the rain demonstrated to many Cubans his commitment to the new, warmer relationship.
What else is in store?
Later on Monday, President Obama is due to get down to the nitty gritty of politics with Cuban leader Raul Castro.
Their meeting at the Palace of the Revolution will be closely scrutinised for signs of how much practical progress has been made.
Ahead of the meeting, President Obama said he believed that "change is going to happen here and I think that Raul Castro understands that".
He also told US broadcaster ABC that he would be announcing that Google had made a deal with the Cuban authorities to expand Cuba's poor wifi and broadband access.
There have been a series of other agreements between the two countries since the thaw was announced, including commercial deals on telecoms and a scheduled airline service, increased co-operation on law enforcement and environmental protection.
Many Cubans are hoping their economy will receive a further boost from further openness and reforms as well as US investment.
Cuban officials are banking on a growth in US tourists visiting the island as restrictions on US citizens travelling there are eased further.
On Sunday, US hotel company Starwood announced it had become the first US firm to agree a deal with the Cuban authorities since the revolution of 1959.
The company said it would be making a "multimillion-dollar investment" to bring three Cuban hotels "up to our standards".
While President Obama's agenda was carefully discussed with Cuban officials, one thing the White House has insisted on is a meeting between the president and Cuban dissidents, whether the Cubans like it or not.
Among them are expected to be members of the Ladies in White, a group which campaigns for the release of political prisoners.