She was born in Tbilisi. She started her musical study at the Music school named after P. Paliashvili and then she studied at the P. Tchaikovsky Music School, Yerevan. She graduated from Yerevan Komitas State Conservatory as a pianist (associate professor I. Sedrakyan) and organist (prof. V. Stamboltsyan).
As an organist, harpsichordist and pianist, she has been working in "Tagharan" Ancient Music Ensemble (Artistic Director and conductor S. Erkanyan). She is a educational assistant at the Opera Studio of Yerevan Komitas State Conservatory.
With "Tagharan" ensemble and other groups she has toured in Germany, France, Austria, Yugoslavia, Argentina, Brazil, Uruguay, Turkey, Lebanon, Russia, Estonia, Latvia, Lithuania and other countries.
From 2001, Teresa Voskanyan has been participating in monthly organ concerts at Komitas Chamber Music Hall, as well as in the "Museum Night" concerts at the Cathedral of Holy Etchmiadzin. Since 2013, she is the organist of the Cathedral of Holy Etchmiadzin.
Teresa Voskanyan cooperates with Armenian Philharmonic Orchestra, National Chamber Orchestra of Armenia, National Chamber Choir of Armenia, “Hover” State Chamber Choir of Yerevan.
She is the first performer of organ works by a number of Armenian composers (Yer. Erkanyan, D. Saqoyan, Zh. Shahrimanyan...).