The 64-year-old was rushed to Aberdeen Royal Infirmary in a critical condition just over a week ago.
However, television presenter daughter Kirsty wrote on Twitter: "Thank you all so much for your kind messages of support, it's been quite overwhelming. Dad now making a good recovery.
"We are all so grateful for the fabulous support we've had, it's kept us going."
Gallacher made the first of his eight Ryder Cup appearances as a player in 1969, the same year he became the youngest winner of the PGA Championship at 20 years and 97 days - a record which stood until earlier this year when Italian Matteo Manassero triumphed at Wentworth aged 20 years and 37 days.
He went on to win 10 European Tour titles but is perhaps best known for his role as Ryder Cup captain in 1991, 1993 and 1995.