The 64-year-old Scot collapsed after dinner at the five-star Marcliffe Hotel in Aberdeen on August 29 and was rushed to Aberdeen Royal Infirmary in an ambulance.
He was in a "critical" condition until last Tuesday and daughter Kirsty, yesterday confirmed her father is on the road to recovery.
She tweeted: "Thank you all so much for your kind messages of support, it's been quite overwhelming.
"Dad now making a good recovery. X" In reply to Sky Sports pundit Denis Pugh she added: "We are all so grateful for the fabulous support we've had, it's kept us going!"
Gallacher is best known for his role as Ryder Cup captain, in 1991, 1993 and 1995. Europe narrowly missed out on his first two contests, but his team finally won the trophy back in 1995.