0502 GMT October 19, 2019
The 23-year-old's move beats Sporting's sales of Cristiano Ronaldo (£12.24 million) and Nani (£25 million) to Manchester United, BBC reported.
It is also the second-biggest move out of Portugal, marginally behind the fee Monaco paid Porto for Colombian James Rodriguez in 2013.
Inter remains in talks over signing Brazilian Gabriel Barbosa from Santos.
Inter president Erick Thohir said, "Mario is a very important player, who we have followed for a long time and who would enforce an already competitive squad."
Midfielder Mario made 171 appearances for Sporting and played in every game of Portugal's Euro 2016 triumph, when it beat France 1-0 in the final.