John Adams was the first president to live in the White House. While George Washington oversaw the construction of the White House, he never actually lived in it. He left office before it was completed. John Adams moved into the White House with his family on November 1, 1800, shortly after the building was finished.
It's worth noting that the White House was not originally called the White House. It was originally known as the President's House. It was only later, in the 19th century, that it became known as the White House.