Mr Gallacher, 64, was admitted to Aberdeen Royal Infirmary on 29 August after collapsing at the luxury Marcliffe Hotel on the outskirts of the city.
He was first said to be in a “critical” condition but last week Mr Gallacher was showing signs of improvement and had been described as “stable” on Friday in the latest update on his condition issued by hospital authorities.
But today daughter Kirsty, a Sky Television sports presenter, posted on Twitter: “Thank you all so much for your kind messages of support, it’s been quite overwhelming. Dad now making a good recovery.”
A new hospital update on Mr Gallacher’s condition is expected later today.
Mr Gallacher is believed to have been taken unwell at a dinner at the luxury Marcliffe Hotel in the Cults area of Aberdeen, following an appearance at an event at Banchory Golf Club. An ambulance was called to the hotel to rush Mr Gallacher to hospital.
He began playing golf when he was only eleven and won the 1967 Scottish Amateur Open Stroke Play Championship before turning professional the same year and going on to win the Sir Henry Cotton Rookie of the Year Award in 1968.
In 1969, at the age of 20, he became the youngest player to represent Great Britain and Ireland in the Ryder Cup up to that time. He also recorded his first win as a professional that year, taking the PGA Championship title.
He played in the Ryder Cup eight times and was non-playing captain of the European Team in 1991, 1993 and 1995. He lost the first two matches but led the European side to a stunning victory on American soil in 1995 when the European team beat America by 14½ to 13½ points at the Oak Hill Country Club in Pittsford, New York.