Alekseyev was the son of an officer, who had started his career as a private. He entered the Russian Army in 1873. He graduated from the Moscow Infantry School in 1876 and the Nicholas General Staff Academy in 1890. A participant of the Russo-Turkish (1877–1878) and Russo-Japanese wars. During World War I, he was Chief-of-Staff of the Southwestern Front (1914–1915), Commander-in-Chief of the armies of the Northwestern Front (March – August 1915), and the Western Front (August 1915). He led the “Great Retreat” of the Russian Imperial Army (1915) and managed to avoid the potential encirclement and destruction of the retreating troops in the territory of Poland. Since August 1915, Alekseyev held the post of Chief-of-Staff of the Stavka [Headquarters]. He directed all military operations, except those conducted in the period from November 1916 to February 1917, General of Infantry of the General Staff (1914), Adjutant General (1916).

On the eve of the February Revolution, he maintained contact with representatives of the liberal opposition. After the overthrow of the monarchy, he swore allegiance to the Provisional Government. In April–May 1917, he was the Supreme Commander-in-Chief of the Russian Army. He opposed the Soviets and the democratization of the army. A founder of the Union of Army and Navy Officers. On August 30, 1917, Alekseyev became Chief-of-Staff of the Stavka under Commander-in-Chief Aleksander Kerensky. After the failure of the Kornilov affair, he arrested General Lavr Kornilov and his supporters, saving them from the revolutionary soldiers. He sent them to Bykhov under the protection of reliable troops. A few days later, he resigned.

On the eve of the October coup of 1917 and after it, he made effort to form core personnel for a new army (Alekseyev’s Officer Organization), which would be capable of fighting the Bolsheviks. He fled to Novocherkassk, where he published an appeal to the officers (in early November 1917) urging them to “save the Motherland”. Later, he was joined by General Kornilov, who had arrived at the Don.

In December 1917, he joined the Don Civil Council, established in November 1917 in Novocherkassk to lead the anti-Bolshevik forces. The Alekseyev’s Officer Organization became the core of the Volunteer Army (established in December 1917). Alekseyev himself became the Supreme Leader and took charge of political and financial matters, foreign relations, and the organization of the anti-Soviet underground. Alekseyev took part in the First and Second Kuban campaigns (1918). On October 8, 1918, he died of pneumonia and was buried in Yekaterinodar. During the retreat of the White troops in 1920, Alekseyev’s remains were taken to Serbia and reburied in Belgrade.