The Foreign Secretary also told the Commons that Team GB has become a "sporting superpower" as he backed calls for Scotland to stay within the Union.
Glasgow hosts the 2014 Commonwealth Games, which starts next month, where Scotland, England, Wales and Northern Ireland each have teams, whereas at the Olympics athletes from the four countries compete for Great Britain.
Asked what his department is contributing to the preparations for the games, Mr Hague told MPs: "The FCO (Foreign and Commonwealth Office) is playing a strong role supporting the 2014 organising committee.
"Our high commissions across the Commonwealth are also drawing on our contribution to London 2012 to ensure Britain makes the maximum impact from what I am confident will be another spectacular performance by Team GB."
Sir Menzies Campbell, a Scottish MP and former Liberal Democrat leader, told Mr Hague: "Perhaps I'll just remind you that, of course, the constituent parts of the United Kingdom compete in their own right and so there will be a Scottish team, a Welsh team, an English team and a Northern Ireland team."
Team GB secured 63 medals at the 2012 London Olympics, including 28 gold, 17 silver and 18 bronze.
In 2010, at the Commonwealth Games in Delhi, England won 143 medals while Scotland picked up 26, Northern Ireland 10 and Wales 19.
Speaking during Foreign Office question time, Conservative Richard Drax (South Dorset) turned to Scottish independence ahead of September's referendum.
He asked Mr Hague: "Do you agree with me that the preparation of these games by the city of Glasgow and both the Scottish and UK governments is a prime example of how well we all work together, and how important it is we remain a United Kingdom to ensure that 300 years of history, union and cooperation continue in the years ahead?"
The Foreign Secretary replied: "You are absolutely right. It is another example of how Scotland has the best of both worlds.
"Scotland is the proud host nation for the Commonwealth Games but the UK is the host Commonwealth member state, and we're working together on this very successfully.
"We're confident that the games will be a success and together in Team GB we have become a sporting superpower in the world, and it's very important we keep working together on sport."