Newcastle United agreed to a future sell on clause on Bruno Guimarães in order to secure his services.
French side Lyon will also be entitled to a bonus package should Newcastle stay up and progress in the next few years.
After landing the Brazil international, Lyon stated: "Olympique Lyonnais announces the transfer of Brazilian international midfielder Bruno Guimarães to English club Newcastle for a total amount (including bonuses)* of €50.1 million, as well as a 20% sell-on fee.
Read more: Newcastle complete deal for Bruno Guimarães, as Eddie Howe tells of delight
"The €8 million in potential bonuses takes into account Newcastle's performance over the next few seasons, in particular, its retaining its place in the Premier League, starting this year.
"Additionally, as agreed upon during the Brazilian's initial transfer, 20% of the total transfer fee will be passed on to his former club, Athletico Paranaense."
But the French side wished the midfielder well after selling him, they said: "We would like to warmly thank Bruno Guimarães for his involvement, his determination and his professionalism since his arrival at OL two years ago.
"The whole club wishes him and his family all the best in Newcastle as well as with the Brazilian national team, who have already qualified for the next World Cup in Qatar."