A statement from Premier League giants Liverpool issued a fortnight ago said Hansen was "seriously ill", sparking an outpouring of support for the 68-year-old Reds great and former television pundit.
But his condition appears to be improving and Hansen will now continue his recovery at home, with his family issuing a statement thanking fans for their good wishes.
"Alan has been discharged from hospital today (Sunday) to continue his recovery at home," the statement said.
"Alan, Janet, Adam, Lucy and family would like to thank everybody for their wonderful messages of love and support. It has been overwhelming and has helped enormously.
"We also hugely appreciate the ongoing respect that has been shown for our privacy as Alan continues his recovery. Thank you."
Earlier in the week, Hansen's former Liverpool and Scotland team-mate Graeme Souness gave a positive update on Hansen's condition.
"I spoke to him and he sounded fabulous so I hope that's him on the way to a full recovery," Souness told talkSPORT radio.
"He's definitely back because he did nothing but take the mickey out of me.
"He's been in a difficult place but the way he sounded, he's back, and I hope I'm right."
Hansen joined Liverpool from Partick Thistle in 1977 and won three European Cups, eight league titles, two FA Cups and three League Cups in 620 appearances for the Anfield club.
An elegant central defender, he won 26 caps for his country and was a member of Scotland's 1982 World Cup side.
After retiring from a hugely successful playing career in 1991, Hansen went on to become a well-known television pundit, notably on the BBC's flagship Match of the Day programme.
