Alchevsky graduated from the Faculty of Physics and Mathematics of Kharkiv University in 1887 and went on to study at the Moscow Imperial Conservatory.

He wrote a symphonic poem, Alyosha Popovych, while his work Breathing Tables for Singers and their Application to the Development of the Basic Qualities of the Voice, first published in 1908, remains in print.

[2] Gregory's younger brother Ivan Alchevsky [uk] became an opera singer, an orchestral conductor, and a pianist.

[2][7] Alchevsky's students included the singers Dmitry Aspelund, Nicholai Ozerov [ru], and Sergei Yudin.

His most popular works were his settings of folk songs and his two cycles of romances, which were published privately in Moscow by the Kharkiv-born singer Mikhail Slonov [ru].

His romances perpetuated the use of traditional Ukrainian folk songs in classical music, although his settings of Russian texts, such as "Sosna" by Lermontov, "I long stood motionless" by Afanasy Fet, and "I know what father has on these shores" by Maykov, more noticeably show the influence of Russian composers, in particular Pyotr Ilyich Tchaikovsky and Taneyev.

[14] In 1904, Ilya Slatin [uk] conducted the premiere of Alchevsky's symphonic poem Alyosha Popovych in Kharkiv.

[7] Western European romanticism influenced the classical music produced by Ukrainian composers, who similarly adopted historical, oriental, and fairy-tale themes.

[15] According to one review written not long after the piece was performed, it displayed "bold, original talent, melodic gift, a lot of imagination, clarity of musical speech and brilliant instrumentation technique".

[16] Alchevsky's romances were written for solo voice with piano: Alchevsky's methodological teaching aids Vocal Technique in Daily Exercises (1907, Moscow) and Breathing Tables for Singers and their Application to the Development of the Basic Qualities of the Voice (1908, 1928, 1930, Moscow) have been used by musicians for over a hundred years.

[11] The 2015 HUP International Festival ("S. Rachmaninov and Ukrainian Culture") in Kharkiv commemorated Alchevsky's 150th anniversary as part of its celebrations.