Anne Veski (born Anne Vaarmann; February 27, 1956) is an Estonian pop singer who has recorded music in both her native language as well as Russian.

Anne Veski was born as Anne Vaarmann in Rapla, Estonia. She graduated from the musical school in the town, after which she entered the Tallinn University of Technology. Upon finishing her education, she became a professional singer and started working as a soloist with the ensembles Mobile and Vitamiin. Her first notable Estonian language hit song was "Roosiaia kuninganna" ("Queen of the Rose Garden") in 1980. Other prominent Estonian hits were "Troopikaöö" ("Tropical Night") in 1979, "Viimane Vaatus" ("Last Act"), in 1983 and "Jääd või ei?" ("Will You Stay or Not?") in 1986.

Having organized the ensemble Nemo, Veski began her solo career in 1984. In that same year, she participated in the Sopot International Song Festival in Poland. In the contest, she received First Awards in two categories: the Amber Nightingale for the best performance of a Polish song (with the entry "Polka Idolka") and the Intervision Song Contest for the song "Nadezhda gasnet". The Intervision First Prize was in fact a runner-up position, as the winner Krystyna Giżowska received the Grand Prix.

Popular Russian language songs in her repertoire include "Vozmi menya s soboy" ("Take Me With You"; 1983), "Milyy, goryacho lyubimyy" ("My Darling Beloved One"; 1994) and "Radovat'cya zhyzni" ("Enjoy Life"; 2001).

In 1987, Veski performed in the Estonian rockumentary Pingul keel (Tightened String) with other such notable Estonian singers and musicians as Urmas Alender, Ivo Linna and Tõnis Mägi.

In the beginning of the 1990s, Veski and V. Dovganiy organized a collection of fur clothing for sale in Tallinn and Moscow.