Sauron was a higher bring/spirit, and he has th abilty to take different shapes and form when he needed to. There are many instances where he took different forms.
"wrought for himself a new shape; and it was terrible, for his fair semblance had departed for ever when he was cast into the abyss at the drowning of Numenor. He took up again the great Ring and clothed himself in power" -The Silmarillion.
And in FACT, Sauron could take shape again in the third age
'Yes, He has only four on the Black Hand, but they are enough,' said Gollum shuddering' (The Two Towers: The Black Gate is closed)
AND TO back up the answer to the question
And much of the strength and will of Sauron passed into that One Ring; for the power of the Elven-rings was very great, and that which should govern them must be a thing of surpassing potency; and Sauron forged it in the Mountain of Fire in the Land of Shadow.Silmarillion, Of the RIngs of Power and the Third Age
So when the ring was destroyed, he lost a great deal of his spirit, and was thus himself, vanquished from the physical world.And he wasn't destroyed completely, he was reduced to an impotent spirit that could not again have a physical body, nor cause mischief.