First Minister accepted the symbolic silver putter on behalf of Gleneagles as the host venue, and Scotland as the host country, for the 2014 event.
Last night's ceremony was watched in an estimated 500 million homes in 183 countries worldwide and featured a live performance of Scottish music by classical violinist Nicola Benedetti and Gaelic singer Julie Fowlis, who was recently heard in cinemas as the lead vocalist in the hit Disney/Pixar movie Brave.
A video titled Scotland's Getting Ready was also shown, depicting golf being played in various Scottish landmarks, including Glencoe, chipping into whisky barrels in a distillery and children honing their skills on the Old Course at St Andrews.
It is hoped staging the competition will be worth £100 million to the Scottish economy, five times the £20m investment of public money that has been provided to bring the event to Scotland for the first time in 40 years.
Mr Salmond addressed the crowd, saying: "As First Minister it is my pleasure to invite all golf fans, here today and watching round the world, to share that feeling and come to the Home of Golf – Scotland. Golf is coming home and so is the Ryder Cup. For it was in Gleneagles in 1921 that the first international match was played which inspired the Ryder Cup. But whether you come to Scotland before, during or after 2014, I assure you, you will feel the vibrancy of our culture, the awesome beauty of our landscapes and, above all, the warmth of our welcome."
Mr Salmond also handed over a commemorative version of a historic document that contains the earliest known written evidence of the game of golf to Tony Graffia, president of the Medinah Country Club, in recognition of its position as host of this year's Ryder Cup.
VisitScotland are also counting on a tourist boost off the back of the publicity to be gained from staging the Europe v America clash, and will be running a dedicated marketing campaign to capitalise on Scotland's status as the "home of golf".
Dr Mike Cantlay, chairman of VisitScotland, said: "There is no doubt 2014 will be a year unlike anything we've ever seen in Scotland with the Commonwealth Games and The Ryder Cup. In sport Scotland plays on the world stage. Our journey to inspire the world to come and see the Home of Golf starts today."
Patrick Elsmie, managing director of The Gleneagles Hotel, said: "We want to ensure that Gleneagles is the backdrop for a truly fantastic Ryder Cup. In Medinah, we have had the opportunity to witness the tournament in action, and learn from our US counterparts but now it's the turn of Gleneagles to be the centre of the world stage. This is a fantastic opportunity to promote Scotland and Perthshire as a destination."