Zinedine Zidane says he feels obliged to return to the Real Madrid job to help restore the success and glory the club deserve as among the best in the world.
The Frenchman replaces Santiago Solari, who was sacked after less than five months in charge.
Zidane, 46, who was part of Real's success story as a player, on his comeback, has agreed to take over until 2022 .
To start with, Zidane, who made history as the only manager to record a back-to-back Champions League success with Real during his three-year stint, said his priority was to end the current season strongly by doing well in the remaining 11 matches.
Zinedine Zidane at his unveiling on Monday, set out his mission on his return to Real Madrid as coach
"The next 11 games are important and we must end the season in the best way," he told the press conference at his unveiling on Monday.
In his first press conference, where he was unveiled by Fiorentino Perez to the press on Monday, Zidane also laid bare his ambitions for the club, aiming to achieve what he did in his first spell as the manager and admitted he was happy to return to Real Madrid 10 months after his shock resignation from the coaching job.
Zinedine Zidane's won the Champions League on three successive times during his first stint as Real coach
The former Real midfielder guided the Los Blancos to three consecutive Champions League trophies in three seasons but surprisingly left in May 2018, after leading the club to a third straight Champions League trophy. On his return, he says he is hungry for more.
Zidane returns 'home'
"I'm very happy to be home. I want to put this club to back where it belongs - and now, back to work tomorrow. When I left the club it was because I needed to leave the club. I think the players needed it because they had won everything. They had won every title.
"A change was needed at that time. Now I have chosen to return because the president called me. I'm very fond of the president... and I'm here again.
"I played here, I defended this shirt. I'm someone who works for this club and now I'm not going to forget what we have won, but there are also things that I didn't do well. Last season, for example, we were out of the league title race early on. I carry a love inside for this club that nobody can take away. I am buzzing."
Asked if his return could also signal the return of star striker, Cristiano Ronaldo, who played a key role in Real's Champions League history, Zidane, said they would look beyond life without Ronaldo now with Italian side, Juventus.
"That's not the point. We have to look at the coming games. Ronaldo is history at this club, the best or one of the best. But at the moment we are thinking about the next 11 games. I had other offers but I didn’t want to be in charge of any other club.
"I wanted to be here at this club and our main focus is to try and end this season as well as possible and then planning for the new season. We will start that from tomorrow."
Real are currently third in La Liga, 12 points behind leaders Barcelona.
Real Madrid president Florentino Perez could not stop Zinedine Zidane from walking away from the job after making history in his 878 days in charge
Perez, who was visibly disappointed when Zidane announced his exit in his presence at a similar press conference last year, was obviously happy to have been able to convince the Frenchman to return to the Bernabeu.
"The best manager in the world has rejoined the club," he told the press conference.
"Our destinies are once again united."
Zidane also admitted that his relationship with both Perez and the club made it impossible for him to say no to the request for him to return to the job he walked away without any explanation.
"When Florentino Perez called me I couldn’t say no. He understands what happens, what managers go through and what players go through and when you’ve won a lot you can have dips in form and that’s what’s happened this year.
"I was looking at it from the outside but I felt like I was part of it because they were my players. I’m not happy at how things have gone here at the club and I know the players feel the same.
"To be a manager of Real Madrid is unique. I know because I have experienced it. I am hungry for more."
Julen Lopetegui succeeded Zidane as Real coach last August, but he did not last
Santiago Solari also struggled to fill the void after taking over from Lopetegui last October
Turbulent season for Real
Solari, who himself replaced Julen Lopetegui last October on a temporal basis, supervised his last match as manager in Sunday's 4-1 win over Real Valladolid.
However, like his predecessor Lopetegui, Solari, was unable to pull an impressive campaign together for Real, the worse, being the shock Champions League exit to Ajax.
That 4-1 home defeat and 5-3 aggregate loss to the Dutch side was the final straw for Perez.
The Champions League elimination followed two consecutive losses to Barcelona in El Clasico - a 1-0 reverse in La Liga and a 4-1 aggregate defeat in the Copa del Rey.