Under the deal, his company, Murray International will feature on the Scottish national team shirts, starting with next season’s Six Nations Championships.
Famous Grouse ended its 17-year shirt sponsorship deal with the Scottish Rugby Union last month.
Sir David Murray said, "It's crucial that business gets behind Scottish sport. When you run a big business in Scotland you also have a social responsibility to support sport and I hope other people take the lead.
Gordon McKie, chief executive of the SRU, said: "This is fantastic news for Scottish rugby just before the team heads off to France for the World Cup.
"It is particularly pleasing that we have replaced one of Scotland's best-known brands with one of Scotland's best-known entrepreneurs who is passionate about, and supportive of, all Scottish sport.
