The move is part of the rapprochement process that was announced by presidents Barack Obama and Raul Castro on 17 December last year.
The two countries have since restored diplomatic ties and reopened embassies.
Cuba and the US began re-establishing postal links in 2013, before the change of policy was announced.
Mail and parcels between Cuba and the US have been re-routed through a third country, usually Mexico or Canada.
In March, direct phone connections with the US were restored after more than 15 years.
Previously, phone calls also needed to go through a third country.
While delays in the postal services have caused frustration for decades, their use in the 21st Century is becoming limited, says the BBC`s Will Grant in Havana.
Couriers carry mail and small packages between Miami and Havana on a regular basis.
And as the communist-run island gradually opens up to the internet, new generations of Cubans are writing fewer letters than their parents and grandparents used to, adds our correspondent.
More about:
