Llorente will undergo a medical before signing a five-year contract at the Wanda Metropolitano in a move understood to be worth an initial €30 million (£26.7m/$33.9m), with the potential for a further €5m to be paid in add-ons.
Further moves are set to follow with a number of high-profile players departing Atleti – including Diego Godin, Juanfran and Lucas Hernandez – and Antoine Griezmann expected to leave.
Rivals Madrid have also been active in the transfer market, bringing in Eden Hazard, Luka Jovic and Ferland Mendy in addition to previous deals for Eder Militao and Rodrygo Goes.
Madrid released a statement to confirm Llorente's imminent move on Thursday.
"The club wants to show its gratitude for all these years of dedication and professionalism and for [Llorente's] exemplary behaviour from when he arrived in 2008 to his trajectory with the first team," it read.
"Real Madrid wishes you good luck on your new stage."
He also made a handful of games in the Champions League, as Los Blancos failed to defend their title after winning three crowns on the bounce.
Signed to the Madrid youth system in 2008, he made his debut for the club in October 2015 as a substitute and scored his first goal last December against Al-Ain in the Club World Cup final, in which he was named man of the match.
His limited opportunities on the whole at Santiago Bernabeu has arguably cost him the chance of a senior call-up, with Llorente having played at under-19 and under-21 level for his country.
He leaves with two years remaining on his contract, having initially signed an extension in September 2017 that took him through until the end of the 2020-21 season.