Redpath's father was a tweed designer in the Scottish Borders. She saw a connection between his use of colour and her own. "I do with a spot of red or yellow in a harmony of grey, what my father did in his tweed." The Redpaths moved from Galashiels to Hawick when Anne was about six. After Hawick High School, she went to Edinburgh College of Art in 1913. Post-graduate study led to a scholarship which allowed her to travel on the Continent in 1919, visiting Bruges, Paris, Florence and Siena.
The following year, 1920, she married James Michie, an architect, and they went to live in Pas-de-Calais where her first two sons were born; the eldest of whom is the painter and sculptor Alastair Michie. In 1924, they moved to the South of France, and in 1928, had a third son: now David Michie the artist.
In 1934, she returned to Hawick. Redpath was soon exhibiting in Edinburgh, and was president of the Scottish Society of Women Artists from 1944 to 1947. The Royal Scottish Academy admitted her as an associate in 1947, and in 1952, she became the first woman Academician. In 1955, she was made an OBE for her work as "Artist" and "Member of the Board of Management of the Edinburgh College of Art".
With her children grown up, and an active involvement in Edinburgh art circles, she moved to live in town at the end of the 1940s. In the 1950s and early 1960s, she also travelled in Europe, painting in Spain, the Canary Islands, Corsica, Brittany, Venice and elsewhere.
There is a commemorative plaque on the house where she lived and entertained in London Street, Edinburgh.
During her years in France (1920–1933), Redpath's painting was limited by family commitments, but she produced enough for exhibitions in 1921 and 1928. She also decorated furniture with bright flower and bird patterns. (See Still Life with Painted Chest) Later there would be many paintings of flowers: in vases, or growing abundant in the wild. (The Poppy Field) Redpath became heavily influenced by the likes of Matisse and Bonnard.
On her return to Scotland in 1934, she started to sketch the countryside round Hawick, and painted landscapes with a more muted look than much of her work: Frosty Morning, Trow Mill (1936), for example. In the early 1940s The Indian Rug showed that she was developing the freer, individual approach described above. Other works representing this style include The Mantelpiece and Still Life with Table.Window in Menton, painted in 1948, a favourite of Redpath's, is also a richly-textured surface with familiar elements - flowers, chair, printed wallpaper - but here a seated woman looks towards an open full-length window.Redpath painted more hillsides, like Les Tourettes (1962), as she travelled in the later years of her life, but her interest was still often interior. Her Courtyard in Venice (1964) is another view from inside looking outwards.Some later works reflect religious influences, especially paintings of altars in The Chapel of St Jean - Treboul (1954) andVenetian Altar.