Melania and Barron Trump White House Bound in June

Melania and Barron Trump will become full-time residents of 1600 Pennsylvania Ave. in June ... TMZ has learned.

Sources familiar with the situation tell us, contrary to some reports the president's wife and son may stay in NYC indefinitely, we're told they are "absolutely moving after the school year."

We're also told the family has already selected the school Barron will be attending.

The White House staff is already getting ready ... Melania's quarters in the residence are getting a fresh coat of paint.