Anna Mjöll was born in Reykjavík, Iceland. She is the daughter of the guitarist, composer and arranger Ólafur Gaukur and the singer, model and radio program director/producer Svanhildur Jakobsdóttir. She performed on Iceland television numerous times before her 1996 Eurovision appearance where she represented Iceland with the song "Sjúbídú", which she co-wrote with her father.
Following her Eurovision appearance, she toured worldwide with the singer Julio Iglesias for three years. In 2006, she co-wrote and performed three songs with C.J. Vanston for the film For Your Consideration.
In 2009, she released a CD, The Shadow Of Your Smile, containing a mix of Icelandic songs and jazz standards. The CD included a number of notable musicians including Vinnie Colaiuta, Dave Carpenter, Don Grusin, Neil Stubenhaus and Luis Conte, and was voted one of the top 5 female vocal jazz CDs of 2009 at Arnaldo DeSouteiro's Jazz Station. In 2009, Mjöll was voted one of the top 5 jazz singers of the year by DeSouteiro's Jazz Station.
In 2010, she released her first solo Christmas CD, Christmas JaZZmaZ. The CD has original arrangements by Ólafur Gaukur and musicians including Vinnie Colaiuta, Luis Conte, Ólafur Gaukur, Don Grusin, Dave Carpenter and Charlie Bisharat, and was voted one of the top 10 female vocal jazz CDs of 2010 at Arnaldo DeSouteiro's Jazz Station. In 2010, Mjöll was voted one of the 10 best female jazz singers of the year by DeSouteiro's Jazz Station, and Christmas JaZZmaZ was voted Christmas CD of the Year.