Just after midnight local time, the diplomatic missions of each country became full embassies.
The Cuban flag was raised on Monday at the newly opened embassy in Washington.
"Nothing is more futile than trying to live in the past," said US Secretary of State John Kerry.
"We're taking a historic and long overdue step in the right direction."
Despite the historic shift, both sides admit to lingering difficulties.
There were still "issues that we don't see eye to eye on", a US state department spokesman said.
A flag will not be raised at the American Embassy in Havana until Mr Kerry pays a visit there on 14 August.
Bruno Rodriguez, Cuba's minister of foreign affairs, called for a removal of the 53-year-old US trade embargo and for the US to return Guantanamo Bay to Cuba.
"I will welcome Mr Kerry in a few weeks and continue talks," Mr Rodriguez said.
Outside of the embassy, crowds of people cheered as the Cuban national anthem played and three Cuban soldiers stood at attention while the flag was raised.
Protesters dotted the crowd, and one was removed from the area by police.
Mr Obama's efforts to engage Cuba were partly held back by the country's imprisonment of US Agency for International Development contractor Alan Gross, who was jailed for espionage charges. Secret negotiations led to Mr Gross's release last year.
Restrictions on Americans wanting to travel to Cuba remain in place, as does the wider US trade embargo banning most American companies from doing business in Cuba.
Cuba says the embargo - which it calls a blockade - is hugely damaging to its economy.
President Raul Castro has urged President Barack Obama to lift it, calling it the main stumbling block towards normalisations. But the US Congress would have to vote on the issue.
The two presidents announced the move towards diplomatic ties in December last year.
Conrad Tribble, deputy chief of mission for the US in Havana, tweeted: "Just made the first phone call to State Dept Ops Center from United States Embassy Havana ever. It didn't exist in Jan 1961."
He then shared the US Cuban embassy's new Twitter account, which already has more than 5,000 followers.
Cuba and the US have formally restored diplomatic relations after an agreement struck last year putting aside decades of hostility came into force.