Luis Fortuno said Puerto Rican voters embraced statehood and rejected the current US commonwealth status in the November 6 ballot.
He said Congress and Mr Obama pledged to respect the results.
In the first question of the two-part referendum, more than 900,000 voters, or 54%, said they were not content with the commonwealth status.
The second question asked what status was preferred. Of the about 1.3 million voters who made a choice, nearly 800,000, or 61%, supported statehood. Some 437,000 backed sovereign-free association and 72,560 chose independence. But nearly 500,000 left that question blank, complicating analysis of voter sentiment.
Another complication is that voters rejected Mr Fortuno for another term, electing as governor Alejandro Garcia Padilla. His Popular Democratic Party wants to keep Puerto Rico as a semi-autonomous US commonwealth.