The former Manchester United and Aberdeen manager, who has been recovering at home for the past two months, has thanked medical staff in a video message released by the club.
The 76-year-old has also revealed that he intends to be back at Old Trafford to watch United in the coming season.
In the video, Sir Alex said: ““Just a quick message, first of all, to thank the medical staff at Macclesfield, Salford Royal and Alexandra hospitals.
“Believe me, without those people who gave me such great care, I would not be sitting here today.
“So, thank you from me and my family. Thank you very much.
“It has made feel so humble, as have all the messages I’ve had from all over the world wishing me the best, and the good wishes do resonate very, very strongly with me.
“So thank you for that support you’ve given me.
“And lastly, I’ll be back later in the season to watch the team.
“In the meantime, all the best to Jose and the players.”