The 61-year-old was chosen as the replacement for Zinedine Zidane, with Ancelotti leaving Everton after 18 months at Goodison Park.
“I want to thank the president. I’m very happy to come back here, I feel that I’m at home here,” Ancelotti said as he was unveiled at Wednesday’s news conference.
The Italian won the Champions League in his first stint in Madrid between 2013 and 2015, before taking over at Bayern Munich and then Napoli.
“Carlo Ancelotti is not the same as he was six years ago. I’m different, I have six more years of experience. Positive and negative,” he said.
“I was happy at Everton, at a family club. But negative experiences can also make you grow. My first spell here, I remember all that very clearly.
“The matches won, the triumphs, the difficult moments as well, the day of my departure, the day I first arrived.”
“Five years have passed, but coming back here is always something very special,” he added. “I have the same feelings as I had when I first arrived. But now, I’m more certain and more confident.”
Ancelotti brushed off questions about transfer plans and how his team might look next season, saying he “hadn’t had the time to speak with the club”.
However, he admitted he would need to reduce the size of the squad.
“We’re going to see how we’re going to do it. The goal isn’t to sign a striker at any cost who scores 30 goals per season, but to try and find solutions so the wingers or midfielders score a bit more.”
It took less than a week for Madrid to turn the page on Zidane, who ended his less succesful second stint as coach last Thursday, criticising the lack of confidence shown in him by the club hierarchy.
“Everyone here has to thank ‘Zizou’ for the work he’s done. What he’s done is incredible,” said Ancelotti, who worked with Zidane during his initial two-year reign in the Spanish capital.
“I haven’t yet had the chance to speak with him, but I will do soon because he’s a friend.”