Aav was born in Tallinn and graduated from the Estonian Academy of Music and Theatre in 1961. From 1961 he performed at the Estonian Drama Theatre in Tallinn. He played in dozens of films and twenty screenplays and also recorded a number of radio play and audio CDs (including Uncle Remus stories and Alice in Wonderland) as well as a recurring role as Feliks Viss on the ETV dramatic series Õnne 13.
Tõnu Aav's numerous awards include:
- Eva Kübar, Tõnu Aav 70: tahan, et mul oleks teatris rohkem huvitavaid rolle Postimees, 21 January 2009
- Rainer Kerge, Tõnu Aav 70: Jänkuonu, mis sa nüüd teed? Õhtuleht, 21 January 2009
- Maris Balbat, Tõnu Aav: Iga etendust peaks mängima kui elu viimast Maaleht, 22 January 2009