Inter president Erick Thohir says Joao Mario was a long-term target for the club after they confirmed the signing of the Portugal international.
After Sporting confirmed they had sold the 23-year-old for a fee that could reach EUR45million on Saturday, the Serie A side have now announced the deal and revealed he will be presented to the club's supporters later on Sunday.
Joao Mario played in all seven games as Portugal secured Euro 2016 glory last month and his arrival is set to be followed by that of Brazil striker Gabriel Barbosa.
Inter did not reveal the length of the midfielder's contract as Thohir revealed he had been watched at San Siro for a long time.
Thohir said: "We are delighted to have Joao Mario at Inter. He is a top player and we had been tracking him for a long time.
"He will further reinforce what is already a very strong squad."
Club owner Jindong Zhang was impressed by what he saw of Inter's new signing at the Euros.
He said: "I followed Joao throughout the Euros and saw Portugal's victory in the final. Now I hope to see him achieve more success in an Inter shirt."