The measure will require approval from the US Congress, but President Barack Obama has said he will respect the vote.
But it does not return senators to the US Congress and is represented in Washington by a non-voting delegate.
Almost 80% of the island's electorate took part in the referendum, the fourth in the past 45 years.
With almost all the votes counted, almost 54% voted to change the island's relationship with the US.
And in reply to a second question on what future they favoured, nearly two-thirds wanted full statehood.
There are now almost a million more Puerto Ricans in the US than on the island.