Following his US victory Murray hailed the effect Britain's magical sporting summer has had on the country.
He said on Tuesday: "Being around the Olympics and seeing how the nation came together, from the public to the athletes to the press, everyone was just right behind it. Sport has been this huge part of my life since I was a kid and it's been the best summer of sport in my lifetime and I'm sure in most people's. It's been so much fun and I'm just happy I was able to contribute towards it."
It is not yet known whether Murray will take part in a parade for Scotland's Olympic athletes in Glasgow on Friday.
A source close to Murray said he would be taking a few days out following his arrival in London. He will take some time to rest and "get his head right" before deciding what to do next, the source said.
Murray will next compete at the Japan Open on October 1, according to the schedule on his official website. He will be defending the title after beating Spaniard Rafael Nadal in Tokyo last year, where he also took a victory in the doubles tournament alongside older brother Jamie.