Konstantin was born in the small provincial town Lebedyan (nowadays one of the cities of Lipetsk region), in the south of Russia, to a family of merchants. His town had neither theaters nor libraries, not even a high school. In Lebedyan Konstantin spent the years of his childhood and youth. His first piano lessons he received from his home tutor A. F. Meyer.
Konstantin's musical progress made his parents send their 14-year-old son to Moscow to his first instructor Zverev, Tchaikovsky's student and a talented teacher himself who also taught S. Rakhmaninov and A. Scryabin. Since 1888 Igumnov took lessons from A.I. Ziloty (Liszt's student) in Moscow Conservatory. Igumnov continued his education with P.A. Pabst. Igumnov graduated from Moscow Conservatory with a gold medal.
After taking part in Rubinstein Competition in Berlin in 1895, he kept playing on tour numerous successful performances. Since 1899, he was only 26 years old, till the end of his days Igumnov was a professor of Moscow Conservatory. In 1924 he had become its rector, but he decided to retire from this post in 1929, as he was not fond of administration.
In 1945 Doctor of Arts K.N. Igumnov was awarded Lenin Prize. In 1946 he was awarded USSR State Prize and title of People's Artist of USSR. But being a renown artist and teacher he remained a very modest person. In summer of 1947 K.N. Igumnov played his last concert for the citizens of his native town Lebedyan.
Konstantin Igumnov gave his last concert in the Grand Hall of Moscow Conservatory on December 3, 1947. The audience never suspected that the pianist was seriously ill, and that it was his swan-song. Igumnov played his favourite composers - Chopin, Tchaikovsky, Beethoven; he played five encores. Three months later, Konstantin Nikolayevich Igumnov died.