The US Agency for International Development said it had reached a deal with the company that employed Alan Gross at the time of his arrest.
His release triggered an announcement from the US that it was seeking to restore Cuba relations after 50 years.
Mr Gross was trying to set up internet access for the island's small Jewish community under a USAID programme.
He was arrested, accused of subversion and sentenced to 15 years in prison.
USAID said it had reached agreement with Development Alternatives Inc of Bethesda, Maryland, in an attempt to head off further claims.
A spokesman later said the sum was $3.2m.
Mr Gross, 65, and his wife filed a suit against the US government for negligence, saying he had been sent into a situation known to be dangerous.
But in November a federal appeals court upheld the dismissal of that suit, saying the government was immune from any claim arising in a foreign country.Relations between the US and Cuba have remained frozen since the early 1960s, when the US broke off diplomatic relations and imposed a trade embargo after Cuba's revolution led to communism.
But President Barack Obama said the US was looking to open an embassy in Havana in the coming months, as part of the wider effort to bring Cuba out of isolation.
Mr Gross's release was part of a deal that included the return from the US of three Cubans convicted of spying.
An unnamed spy imprisoned in Cuba went the other way, back to the US.
