The 19-year-old, who joined Atletico's academy in 2007, has penned a six-year contract at the Bernabeu.
The left-back's deal at Atletico ran until the summer of 2021 but he frequently expressed his desire to make the switch to Real.
He impressed on loan at Alaves last season, making 32 La Liga appearances for the Basques and scoring a stunning consolation in the 3-1 King's Cup final defeat by Barcelona - ironically at Atletico's old Vicente Calderon stadium in his only competitive appearance there.
The Champions League winners declined to disclose the details of the deal but it understand that they had to pay a touch more than the Frenchman's €24m (£21m, $27m) release clause to avoid damaging their relationship with their local sparring partners.
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She was eventually told she would be playing on No 1 Court late into the day, with her match not getting underway until 7.13pm. No. 8 seed Dominika Cibulkova ousted her opponent American Jennifer Brady 6-4, 6-4 to advance to the next stage, as well.
Madrid's official website adds that Theo, 19, will be presented to the media on July 10, following his medical.
In their own statement, Atletico explained that Hernandez, who was still under contract until 2021, "repeatedly rejected" the offer of new terms to commit to the club.
"The player, who has never made debut with our first team in official match, has rejected the proposals of renewal of our club and the offerings of other European clubs", it read.
News of Hernandez's arrival at the Bernabeu coincides with the loan departure of Portugal worldwide Fabio Coentrao to Sporting CP earlier on Wednesday. The left back had been linked to a move to Real Madrid for several months.