The $70m (£44m) fibre-optic cable arrived from Venezuela in February 2011, but tests on the line are said to have begun only this month.
Cubans currently rely on expensive and slow satellite links to go online.
The company has already warned that high-speed browsing is unlikely to become widely accessible overnight.
Investments will first have to be made in Cuba’s infrastructure, Etecsa says, so that access can be increased “gradually” and for “social purposes”. Government and research institutions are expected to be the first beneficiaries of the new connection.
But the start of the operation of the Alba-1 cable could herald a major opening-up in Cuba, where the media are state controlled and satellite TV illegal, says BBC Havana correspondent Sarah Rainsford.

Dissident blogger Yoani Sanchez writes about life in Cuba under the current government
A black market exists for internet access, as with many things in Cuba, says our correspondent. Information, music and films are regularly downloaded and shared on flash drives.
Official statistics show that 2.6 million people were online in 2011, the last year for which statistics are available.
But Cuban figures for internet access include users of the heavily-censored government intranet, which limits users to certain pages such as email or those relevant to their work, adds our correspondent.
Despite a number of obstacles and restrictions, though, a blogging community of both dissidents and government supporters is flourishing in Cuba.
Dissident blogger Yoani Sanchez rose to prominence when she wrote about life in Cuba, emailing her blog entries to friends abroad to publish online. Her writing led to her arrest in October last year as she prepared to cover the trial of politician Angel Carromero. The high-speed Alba-1 cable is a joint project between the state-owned telecommunications companies of Venezuela and Cuba.
Although it arrived in in eastern Cuba in 2011, the state telecom company had kept quiet about it until now. The government in Havana blamed the US trade embargo for preventing a link-up to existing American underwater cables. (BBC)