The ex-Manchester United manager, 76, has been recovering after having emergency surgery in May.
In a video posted online by his former club, he said: “Hello, 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 have 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’s made me 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.”
Sir Alex said he would be “back later in the season to watch the team”, and wished “all the best” to current United boss Jose Mourinho and the players.
United striker Marcus Rashford tweeted that the former manager was “looking well” after the video was published.
Messages of support from the world of football and beyond poured in for Sir Alex following news that he was in intensive care.
Ex-United star Cristiano Ronaldo told his former manager to “be strong”, while David Beckham urged his ex-boss to “keep fighting”.
A host of football clubs also voiced support for Sir Alex including United’s rivals Manchester City and Aberdeen, where he managed for eight years.
Sir Alex had appeared on the pitch at Old Trafford a week before he was rushed to hospital to present outgoing Arsenal manager Arsene Wenger – his long-time rival – with a trophy recognising his career.
He retired from managing United in 2013 after 26 years in charge and remains the most successful manager in British football history.
At United, he won 13 Premier League titles, two Champions League crowns, five FA Cups and four League Cups.