The versatile 21-year-old only joined Porto from Sao Paulo last summer, but has impressed considerably in his debut season in Europe.
A statement released by Madrid on their official website read: "Eder Gabriel Militao is officially a new Real Madrid player, signing until 2025".
The centre-back is the Spanish giants' first signing since Zinedine Zidane returned to the club as coach for a second spell this week.
"He comes to the Whites from Porto, where he has quickly become a star of the team in only his first year in the Portuguese League".
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"Multi-purpose player, Militao plays central, although he has also occupied the right-back position". Militao was named as the best defender in the competition for five consecutive matches.
The €50m fee represents a huge profit for Porto, who signed Militao from Brazilian club Sao Paolo last summer for just over £6m.
The Brazilian will arrive in the summer and means that Los Blancos now have four centre-backs they can rely on.
He has scored three goals and picked up two assists in 34 appearances for the Portuguese side, with his displays catching the eye of Madrid.
"His speed, positioning and anticipation are his greatest assets, while he is also strong in the air".
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