Hryhory was the son of a mining engineer, industrialist and banker Oleksiy Alchevsky, and teacher Krystina Alchevska. Hryhoriy also had two sіblings named Ivan and Krystia. Ivan Alchevsky became a renown opera singer and Kristia was a respected poet. Hryhory Alchevsky himself, worked as a teacher of voice and piano, composer and singer. He was a graduate of the Moscow Conservatory of Music. His works include: several textbooks for vocalists, a symphony called "Oleksiy Popovych" (after the character of a Ukrainian duma), arrangements of Ukrainian and Russian folk songs, and a series of solo works to the words of Taras Shevchenko, Ivan Franko, Lesia Ukrainka, and also his sister Krystyna Alchevska.