The composer Judith Weir, 60, will be named as the successor to Sir Peter Maxwell Davies by Buckingham Palace, the Sunday Times reported.
Weir's appointment comes five years after Carol Ann Duffy was made the first female poet laureate and will be seen as further recognition of women's influence in the arts.
A key role of the master of the Queen's music, who is appointed for 10 years, is to compose ceremonial works for events such as royal weddings and funerals.
Weir, who was born in Cambridge to Scottish parents, was selected by Sir Christopher Geidt, the Queen's private secretary and will take up her post later this summer.
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Some of her music is inspired by medieval history and traditional Scottish stories that she heard when she lived in Glasgow in the 1970s.
"I happened to share a house with a folk musician," she had told the newspaper in a 2008 interview.
In 2005 Channel 4 broadcast her opera Armida about the conflict in the Middle East that she had composed during the Iraq invasion two years before.