The measure will require approval from the US Congress, but President Barack Obama has said he will respect the vote.
The island is currently a US territory, which uses the dollar and whose citizens travel on US passports.
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.
If Congress grants its approval, Puerto Ricans would have the right to vote in all US elections, but would also have to pay federal taxes, something at present they are excused from.

Puerto Rico wants to become the 51th state of the US

Please don't make Pr part of the u.s. i'm not trying to be racisit but all the fucking Pr's from here are ignorant loud obnoxiousness theifs, that have to ruin everything for everyone else!

I feel like they should have to have English as their only official language in order to be considered for statehood.

Please don't make Pr part of the u.s. i'm not trying to be racisit but all the fucking Pr's from here are ignorant loud obnoxiousness theifs, that have to ruin everything for everyone else!