Ole Gunnar Solskjaer says he is "honoured and privileged" to have managed Manchester United but accepts it was time to "step aside".
Solskjaer was sacked as United manager after an "embarrassing" 4-1 defeat at Watford in the Premier League on Saturday, with Paris Saint-Germain boss Mauricio Pochettino the club's first choice to take over next summer.
United have confirmed Solskjaer's assistant Michael Carrick will be placed in temporary charge, with the club also revealing their intention to appoint an interim manager until the end of the season.
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Speaking for the first time since his dismissal, Solskjaer told United's website: "First of all, I want to thank the board and the owners for giving me the opportunity because it's not for everyone and I've had the opportunity.
"I'm so honoured and privileged to have been trusted to take the club forward, and I really hope that I leave it in a better state than when I came.
"It's one of those things you dream of in your life. When you've been a player, when you've been a reserve-team coach, the next job then, the only dream and the only thing you haven't done is to manage the club, and I have now.
"It's been a ball, it's been absolutely enjoyable from the first to the last minute, so I have to thank all the players because since I came in, they're top lads, top people. Some have come, some have gone, but all of them, they've been such an enjoyable bunch to work with.
"The board and the owners have backed me in [terms of] bringing good people in, good players in and I think, or I know, I leave this club with a better squad.
"I think everyone knows I've given everything for this club. This club means everything to me.
"I've made great friends, I've reconnected with some great friends, new staff coming in I've become really good friends with. The other staff that was here when I was there, we're good friends and we have connected and that's what it's about at a club like this.
"With the fans, they have been amazing. From day one at Cardiff until the last one now. [They've been] top, and we'll see each other again."
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'Time for me to step aside'
Solskjaer, 48, signed a new three-year deal in July but leaves United after a run of five defeats in seven Premier League matches saw them fall to eighth place in the table and 12 points behind leaders Chelsea.
The Norwegian's position looked almost untenable following humbling home defeats by Liverpool and Manchester City in recent weeks as his tactics came under intense scrutiny, but it was Saturday's loss to Watford that forced United's hierarchy to act.
Solskjaer achieved third and second-place finishes in his two full seasons in charge but failed to win silverware, with last season's penalty shootout loss to Villarreal in the Europa League final - a year after falling short in three cup semi-finals - his best effort of ending United's four-year trophy drought.
"I wanted us to take the next step to challenge for the league, to win trophies, but unfortunately I couldn't get the results we needed and it's time for me to step aside now," he said.
"Second place last season ahead of arguably one of the best teams in Europe (Liverpool), I think that's a great achievement as well.
"And we were so close in Europe. Sometimes that's the fine margin for you, one penalty."
Ole: I want next manager to be successful
Former Tottenham boss Pochettino is United's first choice to replace Solskjaer on a permanent basis, with Ajax head coach Erik ten Hag understood to be second on the club's shortlist.
Pochettino was heavily linked with United following his sacking by Spurs in November 2019 but eventually joined PSG in January 2021. Sky Sports News has been told Ten Hag would "100 per cent be interested in the job" in the summer, but both men have contracts until 2023.
Solskjaer was United's fourth permanent manager since Sir Alex Ferguson retired in 2013 and lasted longer than more experienced predecessors David Moyes, Louis van Gaal and Jose Mourinho.
"I want him to be successful," Solskjaer said of his successor. "Hopefully I've laid the foundations for that to happen because I know I'm good at what I do.
"I'm 100 per cent sure to create a football environment, that's where I'm good at and at some point, I'll probably be back [working in football].
"I don't want to pre-empt anything but the two times I've left Molde, they've won the league the year after, so all the best to whoever takes over - that's the expectations.
"I know the foundation is there, I know they're ready to kick on and I'm sure they will."
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Neville: Ole couldn't get a performance out of them
Sky Sports' Gary Neville reflects on Solskjaer's dismissal:
"He has always had that result in the past that has pulled him out of the mire when you thought it might get a little bit too tricky for him. But this time the results have just got worse and worse. The worst thing has been the performances.
"Yesterday, some of the defending is absolutely woeful, the goalkeeper, the defenders. It is a back four or back five that have played together a number of times and Watford are not the best team in the league by a long stretch. They mauled Manchester United. Ole could not get a performance out of them in the end. The players looked drained of confidence.
"I am not surprised today that it has ended.
"The worst thing for Ole Gunnar Solskjaer would have been if he had become a bridge for a dark period in the club. Hopefully, it will be a bright future. They need to get the next appointment right. Maybe that will be at the end of the season."
November 23: Villarreal (a) - Champions League, kick-off 5.45pm
November 28: Chelsea (a) - Premier League, kick-off 4.30pm, live on Sky Sports
December 2: Arsenal (h) - Premier League, kick-off 8.15pm
December 5: Crystal Palace (h) - Premier League, kick-off 2pm
December 8: Young Boys (h) - Champions League, kick-off 8pm