Aleksander Krivoshein was born in Warsaw into a family of military officer. His father came from peasants, who earned personal nobility. He started his career as a soldier and achieved the rank of lieutenant colonel. Krivoshein’s mother came from an impoverished Polish noble family. He graduated from the Law Faculty of St. Petersburg University. Since 1887, he worked for the Ministry of Interior, in 1904 he was appointed Head of the Resettlement Administration. Since June 1905, Deputy Chief manager in charge of land management and agriculture. Since May 1906, a member of the State Council. Since October 1906, Deputy Minister of Finance, manager of the Nobility Land Bank and Peasants Land Bank.

In 1908–1915, Chief manager of land management and agriculture (the position was equal to that of a minister). Krivoshein took an active part in the implementation of the Stolypin agrarian reform. In 1915, he was among the ministers, who tried to dissuade Nicholas II from commanding the army. He was forced to resign due to the reaction of Empress Alexandra Fyodorovna, who began to perceive him as an “enemy”.

After the October coup, he was a founder of the Right Center in Moscow (spring 1918). In February–March 1918, he organized fundraising and transfer of funds to the royal family, who were under arrest in Tobolsk (250 thousand rubles).

Krivoshein took part in the organization of the White movement in the South of Russia. At the end of 1918, he was a founder of the monarchist Council for State Unification of Russia (Kyiv, Odessa). In the rear of the Armed Forces of the South of Russia (AFSR), he headed a conservative-liberal group, that criticized Anton Denikin’s entourage for the lack of a well-thought-out social program and other political mistakes. December 1919 – February 1920 saw him hold the post of the Head of the Department for the provision of the government under the Commander-in-Chief Denikin.

After the defeat of the AFSR, he lived in Constantinople, Belgrade, and Paris. In April 1920, Krivoshein agreed to help Pyotr Wrangel, returned to Russia and headed the Government of the South of Russia. His personal contacts and reputation contributed to obtaining support from France for the White Crimea. In November 1920, he emigrated. Krivoshein died in Berlin.