The company, Etecsa, said initially the link would only be for phone calls.
Telephone calls have until now passed through a third country, making them very expensive.
It is the first agreement signed by the two countries since the announcement last December that the two states would renew diplomatic ties.
Americans and Cubans will now be able to make direct calls to each other’s countries.
“The re-establishment of direct communications between the United States and Cuba contributes to providing better infrastructure and better communications quality between the people and our two countries,” Etecsa said.
Etecsa’s American counterpart, New Jersey based telecommunication firm IDT Domestic Telecom, said: “Ultimately, the agreement will make it easier and more affordable for our customers to call friends and family in Cuba.”
According to the Miami Herald newspaper, the two companies were in talks to restart international long-distance traffic between the two countries before the announcement in December.
A key part of the decision of the Obama administration to restore diplomatic ties with Cuba was to help boost telecommunications on the island, the BBC’s Will Grant in Havana reports.
Our correspondent adds that in the long run it is hoped in Washington that it will lead to greater Internet access.
A US delegation led by Daniel Sepulveda, the State Department Bureau of Economic and Business Affairs co-ordinator for international communications and information policy, will head to Havana later this month to meet their Cuban counterparts.
Cuban officials have said they are ready to work with US telecommunications companies.
“We confirmed we are ready to receive US telecom companies to explore business opportunities – business that could be of benefit to both sides,” Josefina Vidal, the Cuban foreign ministry official heading the Cuban delegation, said after the first round of US-Cuba talks in January.
Only an estimated 5% to 25% of Cubans have any type of Internet service.
However, since the December announcement, Cuba has temporarily cut the price of state-run Internet cafes from $4.50 (£3) an hour to $5 for over two hours.
The government has also said it plans to open more than 100 additional cafes this year.
Last year, Etecsa also launched a mobile email service, Nauta.cu.
In February, Netflix announced that Cubans with high-speed Internet connections and access to international payment methods would be able to subscribe to its popular film and TV show service.
However, few Cubans will be able to afford to access their service at the moment.