The record-breaking manager also said he will now be able to enjoy United games rather than "suffer with them", thanking fans, players and staff for their help.
With Paul Scholes also retiring from the club for a second time, Sir Alex praised the midfielder as one of the best players the club has ever had, and wished Darren Fletcher a speedy return to first-team football.
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"This is a thank you to Manchester United. Not just the directors, not just the medical staff, the coaching staff, the players and supporters. It's all of you. This has been the most fantastic experience of my life. Thank you.
"I have been very fortunate that I've been able to manage to some of the greatest players in the country, let alone Manchester United. And all these players today have represented this club the proper way. They won the championship in fantastic fashion. Well done to the players.
"My retirement does mean the end of my life with the club. I'll now be able to enjoy watching them, rather than suffer with them. But, if you think about it, those last-minute goals, the comebacks, even the defeats are all part of this great football club of ours ... so thank you for that.
"I'd also like to remind you that when we had bad times at the club, all the staff stood by me, all the players stood by me. Your [the supporters] job now is to stand by your new manager.
"Before I start blubbing, I just want to speak to Paul Scholes, who retires today. He is unbelievable. One of the greatest players we've ever had and ever will ever.
"I also want to wish Darren Fletcher a speedy recovery and return to the club.
"I wish the players every success in the future You know how good you are, you know the jersey you're wearing and you know what it means to everyone here [at Old Trafford]. Don't ever let yourselves down. The expectation is always there."