President Obama has indicated US policy on Cuba will change
The US Congress has voted to lift restrictions on relations with Cuba imposed by the Bush administration.
Cuban-Americans will be allowed to travel to the island once a year and send more money to relatives there.
Curbs on sending medicines and food have also been eased. The measures were part of a $410bn bill to fund US government operations.
The legislation was approved by the Senate after clearing the House of Representatives last month.
The bill was supported by two Cuban-American senators who had initially opposed it.
They changed their votes after receiving assurances from the Obama administration that the changes did not amount to a major reversal of the 47-year-old US trade embargo on Cuba.
The legislation overturns rules imposed by the Bush administration which limited travel to just two weeks every three years, and confined visits to immediate family members.
President Obama - who needs to sign the bill - has said he supports it.
He has also indicated that he would be open to dialogue with Cuba's leaders.
But he has said that like previous American presidents, he will only consider a full lifting of the embargo once Cuba's communist government makes significant moves such as the holding of democratic elections.
Cuba's President Raul Castro has said he is prepared to negotiate with the new US administration, providing there are no preconditions.
The BBC's Michael Voss in Havana says remittances from Cuban-Americans will provide an important lifeline in a country where the average salary is about $20 a month.