Tubin was born in Torila, Tartu County, Governorate of Livonia, then part of the Russian Empire.

In 1924 he was admitted to the Tartu Higher Music School starting his studies under the guidance of the famous Estonian composer Heino Eller.

Following the Soviet re-occupation of Estonia in 1944, Tubin fled to Stockholm with his wife Erika and sons Rein and Eino.

Here he wrote most of his greatest works, including two operas, symphonies 5–10, a second concerto for violin, one concerto for double-bass and one for balalaika, a piano concertino, much piano and violin music, choir and solo songs etc.

Towards the end of his life, Tubin slowly began to gain recognition, particularly after the conductor Neeme Järvi, also an Estonian, escaped to the United States in 1980.

The shift to a less nationalistic and more international style came after Tubin had fled Estonia to Sweden.

In June 2005 the city of Tallinn observed the centennial of his birth with a festival where all of his symphonies and much of his piano and chamber music was performed.

This has an exhibition about the composer and other members of the "Tartu school" of musicians who studied under Heino Eller including Alfred Karindi, Eduard Oja, Olav Roots and Karl Leichter.