Dobrygin was born in February 17, 1986 in Rybachiy, Vilyuchinsk, Kamchatskaya oblast, RSFSR, USSR (now Kamchatskiy kray, Russia). He studied at a school in Zelenograd, Moscow Oblast. He graduated from the Moscow State Academy of Choreography in the Bolshoi Theatre. In 2010, he graduated from the Russian Academy of Theatre Arts.
His first movies were Black Lightning (2009) and How I Ended This Summer (2010), which got him worldwide recognition.
His first English-language movie was A Most Wanted Man (2014), in which he co-starred with Philip Seymour Hoffman and Rachel McAdams.