"Hello Madrid!" the 61-year-old Italian who succeeds Zinedine Zidane posted on Twitter.
Ancelotti, who won the Champions League for Real Madrid during his first spell at the club between 2013 and 2015, will sign his contract and be presented to the media on Wednesday, the club said in a statement.
It took less than a week for Real Madrid to turn the page on Zidane, who ended his less succesful second spell as coach, last Thursday, criticising the lack of confidence shown in him by the club hierarchy.
Instead, Ancelotti is about to be reunited with the club president Florentino Perez who ruthlessly ousted the coach in 2015, just one year after he led the club to a 10th Champions League title, the long-awaited Decima.
Ancelotti was under contract until 2024 with Everton, but the Italian, whose wife is of Spanish origin has always said he enjoys life in Madrid.
His return is a gesture of appeasement sent to the club's stars.
The heavyweights of the dressing room will welcome a coach adept, like his former protege Zidane, at benevolent and protective management, rather than the more driven approach of Antonio Conte, another Italian contender for the position.
In his first spell at Real, Ancelotti left a favourable impression on fans and players, including Karim Benzema, Raphael Varane, Marcelo and Casemiro, who are still at the club.
He will also be reunited with Austrian defender David Alaba, who played for Ancelotti at Bayern Munich, and is joining Real on a five-year contract.
Ancelotti made history in his first spell at Real by winning the Champions League, after a 12-year gap.
Real trailed neighbours Atletico Madrid going into added time, but Sergio Ramos levelled in the 93rd minute. Then Gareth Bale, Marcelo and Cristiano Ronaldo, with a 120th minute penalty, scored for a 4-1 victory.
Ancelotti also won the Spanish Cup, the European Supercup and the World Club Championship at Real.
But the support of his dressing room was not enough to save Ancelotti when he failed to win another trophy after collecting the World Club Cup in December.
A poll at the time of his departure by Spanish sports daily Marca, which has close to links to the club, found that 73 per cent of club members were in favour of keeping the Italian.
On Tuesday, the club recalled his first stint in charge as a golden era.
"Under Ancelotti's stewardship, the team reigned supreme in Europe 12 years on from the last continental triumph following an unforgettable win over Atletico in the Lisbon showpiece," said the club on its web site, adding: "He is the Real Madrid coach to have recorded the most wins (78) in his first 100 competitive games at the helm."
Real missed the Spanish title last season by just two points and reached the last four in the Champions League, but failed to win a trophy.
Ancelotti will have to rebuild the squad in difficult circumstances.
Real are struggling financially in the face of the Covid-19 pandemic and are consumed by the costly renovation of the Santiago Bernabeu stadium. Real also still face the possible consequences of their refusal to renounce the Super League, which offered the vision of an instant solution to their money problems.
Ancelotti, who joined Everton in December 2019, thanked the English club and its fans "for the tremendous support they have all given me".
"While I have enjoyed being at Everton I have been presented with an unexpected opportunity which I believe is the right move for me and my family at this time," he added in a statement published on Everton's website.
Everton said they would "begin the process of appointing a new manager immediately and will provide updates in due course."