He and Cuban leader Raul Castro agreed to normalise diplomatic relations in December 2014 and in August 2015 the US re-opened its embassy in Havana, more than half a century after it had closed following Fidel Castro's Cuban revolution.
Now reports say that President Donald Trump may announce his new Cuba policy as soon as next Friday.
Many are expecting a rollback on the dÃ©tente including a tightening of the rules on travel and trade eased by the previous administration.
What are the main issues at stake?
This is the area perhaps most at risk.
Every year since the thaw was announced at the end of 2014 has been a record in terms of visitor numbers to the island. In no small part that is down to the large number of US citizens who have been able to come to Cuba since tight travel restrictions were eased.
Opponents of the engagement policy want Mr Trump to adopt proposals which include tightening the 12 categories of travel under which Americans have been coming to Cuba - including the catch-all "people-to-people" exchanges. This would mean US visitors might again face fines if they visit the island without the right paperwork.
The potential effects of such a move on Cuba's tourism industry would be significant. However the pro-engagement lobby group Engage Cuba argues that it would have a multi-billion dollar impact on the US economy too, affecting jobs in the airline and cruise ship industries.
Despite the improved relations, the US economic embargo on Cuba remains firmly in place. As such, bilateral trade between the United States and Cuba is yet to get off the ground.
There have been some initial steps:. In January a shipment of artisanal charcoal became the first legal Cuban export to the US in decades. There was also an agreement for the US hotel company, Starwood, to run three hotels in Havana.
One apparent motivation for any rollback is a desire among Castro-opponents in Florida to reverse Mr Obama's decision to allow US entities to work with Cuban state agencies. The Obama administration felt it was necessary to ease the rules on working with the Cuban state because state-run institutions, specifically the tourism and commercial wings of the Cuban military, are ubiquitous in the Cuban economy.
"That is precisely the kind of dilemma the Trump administration is facing," said Michael Shifter, of the Inter-American Dialogue in Washington DC.
"Initially it sounds easy to take position to roll back Obama's big legacy. But then you see that in Cuba, dealing with state is everything, all economic activity is tied to the state."
Whether it be import-export or transportation, refusing to work with the Cuban military is near impossible in the current climate if you want to establish a sizeable commercial presence in Cuba.
As for the embargo itself, if President Trump chooses to reverse President Obama's policy of engagement, it seems highly likely the embargo will stay in place for the next four years.
The embargo can't be lifted by the president unilaterally, it needs the approval of Congress. However, if a rollback does happen, it would strengthen the hand of the anti-Castro lobby in the House of Representatives and the chances of the measure being removed this term seem slimmer than they did a year ago.
It would be a disappointment for many US businesses hoping to invest in or import to Cuba, but John Kavulich, of the US-Cuba Trade and Economic Council, believes "the US business community as a whole has been preparing for many different scenarios (on Cuba) since the day after Donald Trump was elected".
President Trump has made several references to human rights in Cuba, both as a candidate and since winning the presidency.
Initially it was hard to say whether he was simply appealing to his supporters in Florida or if he genuinely intended to unpick Mr Obama's Cuba legacy using the island's human rights record as his reasoning. It is looking increasingly likely that it's the latter.
After dinner with Florida Senator Marco Rubio in February, Mr Trump said the two men "share very similar views on Cuba". That doesn't bode well for the future of the bilateral relationship as Mr Rubio is keen for President Trump to, in his words, "treat Cuba like the dictatorship it is".
Ironically, the Trump administration's new budget proposals would also remove controversial USAID funding for dissident groups in Cuba, something the Castro government has been calling for for decades.
Given they are the very groups Washington has traditionally heralded as defenders of free speech and human rights on the island, Mr Shifter thinks that the funds may still end up reaching them "through other channels".
This is another arena which has arguably benefitted the most from improved US-Cuba ties.
Whether ballet or jazz, basketball or Beethoven, a greater understanding has been fostered between numerous institutions and individuals in the arts, music, culture and sports. Scores of shared projects have been held since December 2014 partly because obtaining the paperwork has become so much easier.
In science too, Cuban advances in immunology and cancer treatments are undergoing further studies and testing in the United States.
A more hostile footing - and more layers of paperwork - could put such programmes in jeopardy.
Still, while participants on both sides of the Florida Straits are undoubtedly concerned by the prospect of a rollback, many feel confident that their shared projects are now sufficiently well established to outlast any diplomatic cooling.
As one Western diplomat put it, it takes a long time to build trust with the Cuban government - and it can be lost comparatively easily.
On the day of Fidel Castro's death last November, Mr Trump tweeted that the former Cuban president's "legacy is one of firing squads, theft, unimaginable suffering, poverty and the denial of fundamental human rights".
There can be little doubt that the Cubans will remember that line and any subsequent tough stance in order to gain "a better deal" will be met with a typically robust response from the Cubans.
Mr Kavulich believes the Trump administration may well "make an issue" of trying to settle US claims of compensation from the Cuban government over its expropriation and nationalisation policies in the 1960s.
"That would be the deal in his 'Art of the Deal'," he said.
For Mr Shifter though, the danger is that a more hostile tone from Washington would "give bravado to Cuban hardliners to cite it as an example of what happens when we try to open up to the Americans".
Warmer ties with Cuba after almost 60 years of hostility was one of President Barack Obama's main foreign policy legacies.