Hills was born in October, 1953, to a family of missionaries in India and grew up in Michigan. She studied at Interlochen, where she played in a band with Chris Brubeck and Peter Erskine. In 1976, she moved to Chicago and was a co-founder of the record label Hogeye Music. After releasing a few records on Hogeye, the label was bought out by Flying Fish Records in the mid-1980s. In 1984, Anne briefly was a member of a trio (along with Tom Paxton and Bob Gibson) known as the Best of Friends. In 1988 she began collaborating with Cindy Mangsen, with whom she released two duo albums.
Together with Priscilla Herdman the three singers recorded as a trio in 1990 and again in 1997. In 1998, she contributed renditions to tribute albums for Pete Seeger and Phil Ochs. The 2000s saw her collaborating with Tom Paxton and singing in a fourpiece called Fourtold with Steve Gillette, Mangsen, and Michael Peter Smith.
In addition to her musical endeavors, Hills also acts on the live stage. Additionally, she collaborated with Liz Paxson on a children's book with an accompanying album, featuring Hills and her daughter, Tamlyn. She lives in Bethlehem, Pennsylvania, and is married to Mark Moss, editor of Sing Out!.