Born in Tokyo in 1911, Otaka developed an affinity for music from an early age. While attending Seijo High School, he studied piano with Seely Watanabe and composition with Eitaro Katayama. In 1931, he dropped out of high school to study at the Vienna Academy of Music, where he studied piano with Jan Beirl and theory with Stöhr, among others. After studying for a year and a half, he returned to Japan temporarily, where he studied piano with Leo Sirota and composition with Pringsheim, while also teaching music theory at Musashino Music School (now Musashino Academia Musicae).

In 1934, he returned to Vienna, studying with Josef Marx in the master class for composition and with Weingartner in the conducting class at the Academy. His piano piece Japanese Suite, composed in 1936, was later arranged into an orchestral version as his graduation work and received the Weingartner Prize. After graduation, he was active as a conductor with the Vienna Symphony Orchestra and the Berlin Philharmonic.

Upon his return to Japan in 1940, Otaka debuted as a conductor and composer the following year with the New Symphony Orchestra, the predecessor of the NHK Symphony Orchestra, performing his own orchestral works alongside those of Mozart and Brahms. From 1942, he became the permanent conductor of the same orchestra, working devotedly through the chaotic period from the end of the war to the immediate post-war defeat. He also actively pursued creative activities, primarily focusing on orchestral works. He successively premiered many orchestral works with the same orchestra, including Rhapsody for Piano and Orchestra (1943), Symphonic Fantasy "Sōgen" (1944), Cello Concerto (1944), Symphonic Song "Itsukushimauta" (1945), and Concert Suite for Piano and Orchestra (1946). Other works include Sonata for Violin and Piano (1932), Sonatina for Piano (1940), and Piano Trio (1941). His style can be seen as a sophisticated coexistence of German Romanticism and Japanese sensibility.

Otaka subsequently died in 1951 at the young age of 39, triggered by overwork due to the busy wartime and post-war periods. On the first anniversary of his death, the Otaka Prize was established, funded by the prize money from the Minister of Education Award he received posthumously, to recognize orchestral works by Japanese composers. His wife was pianist Setsuko Otaka. His sons, Atsutada, is active as a composer, and Tadaaki, as a conductor.