He was born in the family of a mining engineer in the village of Iultin, Chukotka Autonomous Okrug, Magadan Oblast, former Soviet Union, and spent his childhood in the city of Dniprorudne, Zaporizhia region, Ukraine.
It was the first company with assets in Ukraine whose shares started trading in the main market of the London Stock Exchange and still have premium listings on LSE.
Throughout his career, Kostyantyn Zhevago has held leadership positions on the supervisory and management boards of various Ukrainian and international companies across industries such as mining, metallurgy, machine-building, pharmaceuticals, and food.
He was also the largest shareholder of Avtokraz, where he invested significantly in the development of defense equipment, including the chassis for the Neptune missile complex, which played a pivotal role in the destruction of the Russian Black Sea Fleet's flagship Moscow (Moskva), the wheeled self-propelled howitzer Bogdana, with which it was possible to recapture Zmiiniy Island in the Black Sea, the base for the Verba multiple launch rocket system.
In the 2012 parliamentary elections, he ran for People's Deputy as a self-nominated candidate in 150th single-mandate majoritarian constituency in Poltava region (centered in the city of Horishni Plavni) and won, gaining 61.20% of the vote.
Over the course of his career, he has held senior roles on the supervisory and management boards of numerous Ukrainian and international companies, spanning industries including mining, metallurgy, machinery, pharmaceuticals, and food.
According to estimates by Korrespondent magazine, Kyiv Post newspaper and Dragon Capital company, Zhevago's assets in 2006 amounted to $1.9 billion, he ranked fifth among the richest Ukrainians.
After 3.5 years of trial, on 2 October 2019, the Shevchenko Court of Kyiv ordered to collect ₴1.5 billion from Zhevago in favor of the National Bank of Ukraine.
The decision explains that Kostyantyn Zhevago did not want to fulfill his obligations under the surety agreement to repay the bank's refinancing loans.
According to the inspection data of the Deposit Guarantee Fund, Zhevago and another top manager of the Finance and Credit bank allegedly issued several deliberately bad loans in the amount of almost ₴5 billion in order to get hold of the money.
In addition, according to Zhevago's lawyers, the State Bureau of Investigation has not provided any information regarding this criminal case for many years, which violates his and other accused managers constitutional rights to a fair trial.
On 29 December 2022, the French court of Chambéry ordered the extradition arrest of Zhevago, he was notified of the suspicion of committing criminal offenses provided for in Part 3 of Art.
According to the investigation, in 2007-2010, Zhevago created a criminal organization, which included the chairman, members of the board of the Finance and Credit bank and other persons close to him.
A company controlled by Zhevago received a loan from the bank in violation of the rules, and then the money was subsequently withdrawn to offshore accounts.
Zhevago has been named as the party who allegedly bribed the Chair Person of the Ukraine Supreme Court Vsevolod Kniaziev in 2023.
Zhevago himself was in France at the time of the crime and at the beginning of the investigation, and denies any involvement in this case stating that the accusation is politically motivated.