The musical artist, who has composed everything from grand operas to piano concertos said she hoped to encourage everyone involved in music.
The Queen will hold an audience with Ms Weir at Buckingham Palace tomorrow and say farewell to Sir Peter Maxwell Davies - the previous holder of the post, and who lives in the Orkney Islands.
Ms Weir said: "It is a great honour to take up the position of Master of the Queen's Music, in succession to Sir Peter Maxwell Davies, who has given his musical and personal gifts so freely to this unusual national role.
"I hope to encourage everyone in the UK who sings, plays or writes music, and to hear as many of them as possible in action over the next ten years.
"Listening is also a skill, and I intend to uphold our rights to quietness and even silence, where appropriate."
Ms Weir, whose parents are both Scots, was an oboe player, performing with the National Youth Orchestra, and had composition lessons with John Tavener during her schooldays.
A Cambridge graduate, she has been a visiting professor at Princeton, Harvard and Cardiff universities and during the 1990s was resident composer with the City of Birmingham Symphony Orchestra.
Her music has been described as spare, delicate and beautiful and she draws inspiration from a wide range of sources from folk music from Scotland to Chinese opera.
The office of Master of the Queen's Music is the musical equivalent of Poet Laureate and Ms Weir will serve for a fixed term of ten years.
The post dates back to the Middle Ages.