Andy Murray practises at Wimbledon today
The video message features five cabinet ministers and was recorded for the country's 54 Olympians and 23 Paralympians, whom ministers dub "Scolympians".
First Minister Alex Salmond said: "The eyes of the world are on the Olympics and the whole of Scotland is united in supporting our Olympians and Paralympians, our Scolympians, to go for gold.
"Every member of Team GB has worked exceptionally hard to get to this point and now stands on the cusp of greatness. I wish everyone taking part in London 2012 the very best of luck."
minute-long video, featuring Mr Salmond, Deputy First Minister Nicola Sturgeon, Finance Secretary John Swinney, Justice Secretary Kenny MacAskill and Education Secretary Michael Russell, has been posted on the Scottish Government's website.
In the message, one by one, the ministers say: "London 2012 is here and the whole of Scotland is united in supporting you, Scotland's Olympic athletes, to go for gold.
"We are proud of all 54 Scottish Olympians and 23 Paralympians. You join an elite band of Scottish sporting heroes: from Eric Liddell's movie-inspiring win in Paris in 1924 to Sir Chris Hoy's record-breaking four gold medals. We are proud of the Scottish talent hailing from our shores.
"In June over 450,000 people lined Scotland's streets to see the Olympic flame tour our communities and our most iconic landmarks. Our torchbearers captured the nation's imagination and have been an inspiration to us all.
"The eyes of the world are now on London - and this is your moment. I wish all of you taking part in London 2012 the very best of luck."
The message was released on the eve of the opening ceremony of the Games.
Cycling's Sir Chris Hoy and Wimbledon finalist Andy Murray are two of the Scots hoping to make the country proud.
Sir Chris, from Edinburgh, has four gold medals and a silver from three previous Games. He was recently confirmed as the flag bearer for the British team at tomorrow's ceremony.
Murray, of Dunblane, is the only British tennis player seeded at the Olympics, but he will have to get through a tough first round if he is to make progress in the men's singles.
Swimmer Hannah Miley, of Inverurie, is competing in the 200m and 400m individual medley, while Glasgow's Robbie Renwick will be in the pool for the 200m and 400m freestyle events.
Eilish McColgan, daughter of Olympic 10,000m silver-medallist Liz McColgan, will run in the 3,000m steeplechase.