Born in Los Angeles, the soprano first studied English Literature at Stanford University before earning a Master of Music from Indiana University, Bloomington with Prof. Margaret Harshaw. She attended master classes with Elly Ameling and Regine Crespin and supplemented her studies with Prof. Klesie Kelly-Moog.

Since 2013 she has been professor of voice at the Staatliche Hochschule für Musik Trossingen.  For the winter semester 2019/2020 she was appointed to a professorship for singing at the HfM Würzburg.

She appears as a leading performer in numerous European and American opera houses, as well as at festivals, and as an opera singer has devoted herself primarily to the baroque and classical repertoire. She has sung Handel's Agrippina at Zurich Opera (under Mark Minkowski), Opera Dijon and Opera National de Lille (under Emmanuelle Haim), Teatro Sao Carlos Lisboa and Glimmerglass Opera Festival (under Harry Bicket), and as Rosmene in Handel's "Imeneo" at the Handel Festival Halle, and was acclaimed as Kraus' Prosperpina (in the title role) at the Schwetzingen Festival, as well as Ismene in Cavalli's "Giasone" at the Spoleto Festival.

One of her most brilliant roles is Mozart's Pamina, which she has sung over 100 times, including at the Vienna State Opera, Bavarian State Opera, Frankfurt Opera, Cologne Opera, Deutsche Oper am Rhein, Houston Grand Opera, and New York City Opera.  As Contessa Almaviva, the soprano has been celebrated in Dresden, Marseille, Toulouse, Cologne, Düsseldorf and Pittsburgh, among others.  Her repertoire also includes Mozart's Elettra (Paris and Dusseldorf), Fiordiligi (Paris, Vienna, Düsseldorf and Nuremberg), Donna Elvira(Zurich and Strasbourg), Constanze (Dusseldorf and Essen), Sandrina (Frankfurt), Ismene (Amsterdam) and Celia (San Francisco).

As a sought-after concert singer, Alexandra Coku has worked with many of the world's most renowned orchestras (including the Boston Symphony Orchestra, Chicago Symphony Orchestra, Vienna RSO, Munich Philharmonic, Bavarian Radio Orchestra, Berlin Radio Orchestra). She has appeared at many major festivals, including the Lucerne Easter Festival, the Ludwigsburg Festival and the Dresden Festival.  Her numerous recordings include Schumann's "Paradise and the Peri" conducted by John Eliot Gardiner, as well as Beethoven concert arias with Jérémie Rhorer and two world premieres: the original version of Dvorak's Stabat Mater with piano conducted by Laurence Equilbey, and Eduard Marxsen Lieder with Anthony Spiri at the piano.

Alexandra Coku regularly gives master classes in singing, including at Tongji University, Shanghai, as well as breathing techniques for instrumentalists at the Hochschule für Musik und Tanz Köln and the Conservatorio Superior de Musica Valencia.