The lyrics have undergone some transformation over the years, but the music is still the same tune by James Sanderson from his musical adaptation of Sir Walter Scott’s The Lady of the Lake.
Anyways, a little Google-fu and here are the modern (Albert Gamse) lyrics to the song:
“Hail to the Chief we have chosen for the nation,
Hail to the Chief! We salute him, one and all,
Hail to the Chief, as we pledge cooperation
In proud fulfillment of a great, noble call.
Yours is the aim to make this grand country grander,
This you will do, that’s our strong, firm belief.
Hail to the one we selected as commander,
Hail to the President! Hail to the Chief!”