Chubais was born on 16 June 1955 in the town of Borisov in Belarus, which was then part of the Soviet Union. His father, Boris Matveyevich Chubais, a retired army colonel and veteran of World War II, worked as a lecturer of Philosophy. Though his mother, Raisa Efimovna Sagal, received a degree in economics at university, she opted to stay home to care for their children on the military bases where her husband was regularly assigned. Anatoly Chubais has an older brother, Igor Chubais (born 1947), a Philosopher.

In 1977, Chubais graduated from the Leningrad Institute of Engineering and Economics (LEEI) in present-day St. Petersburg and joined the Communist Party of the Soviet Union until 1991 when he left it. While later working at LEEI, Chubais started a club called Reforma, which helped turn the city of Leningrad into a model of political reform by constructing platforms for both local and national elections. Reforma also engaged in drafting reformist legislation, an important step down the road when Chubais would work in the city government. In 1982, he attained the rank of Associate Professor (доцент) at LEEI, while in 1983, he received his Candidate of Sciences (Ph.D.) degree in Economics for the dissertation entitled "Исследование и разработка методов планирования совершенствования управления в отраслевых научно-технических организациях" (Research and Development of Methods for the Planned Improvement of Management in Industrial Research and Development Organizations).

At the end of 1980, the Economist Vitaly Nayshul proposed the idea of using vouchers to facilitate mass privatization in order to transform the Soviet Union into a market economy. Chubais strongly criticized the scheme at the time, citing the inevitable inequality and social tensions that would result if implemented as proposed. Ironically, Chubais would later become the champion of the same concept just several years later.

By 1987, Chubais had become the organiser of the Leningrad chapter of the club Perestroyka whose mission was to promote and discuss democratic ideas among the local intelligentsia. Among the people involved were his brother, Igor, who had founded the Moscow-based chapter of Perestroyka and Perestroyka-88 clubs, Future Russian Deputy Prime Minister Alexei Kudrin, Future Chubais associates Pyotr Mostovoy and Alexander Kazakov, the Future President of Saint Petersburg bank Vladimir Kogan, Future Minister of Anti-Monopoly Policy and Entrepreneurship Support Ilya Yuzhanov, and Future Deputy Governor of Saint Petersburg Mikhail Manevich.

In 1990, upon the election of Anatoly Sobchak as Chairman of the Leningrad City Council, Chubais assumed the position of his Deputy. He was trying to implement Sobchak's idea of creating a Free Economic Zone in Leningrad. In 1991, Chubais declined the offer to become the Chairman of Leningrad Ispolkom to instead become an advisor to the mayoral administration in Leningrad (by now renamed St. Petersburg) where Sobchak had just been elected mayor. At the same time, Chubais worked as the President of newly established Wassily Leontief Center for Research in Economics.

Chubais originally advocated rapid privatization in order to raise revenue, similar to the model used in Hungary. However, the Congress of People's Deputies of Russia rejected this model. Eventually, a compromise was proposed in the form of a voucher privatization program akin to the program used in the Czech Republic at the time. On 11 June 1991 the Supreme Soviet of Russia adopted this compromise and the massive program was officially initiated by decree of President Boris Yeltsin on 19 August 1991. This privatization program later came under heavy criticism. While most Russian citizens lost their savings in only a few weeks, a few Oligarchs became billionaires by arbitraging the vast difference between old domestic prices for Russian commodities and the prices prevailing on the world market. The people who benefited from this arbitrage became known as "kleptocrats" because they stashed billions of dollars in Swiss bank accounts rather than investing in the Russian economy.

In June 1993, Anatoly Chubais co-founded the electoral bloc “Russia’s Choice”(Vybor Rossii) which was headed by Yegor Gaidar. In December 1993, running under this bloc, Chubais was elected as a deputy to the Russian State Duma in its first convocation.

On 12–13 July 1994 Chubais was elected to the governing council of the party “Democratic Choice of Russia”, which had been built off the electoral bloc “Russia’s Choice”. In December 1998, Chubais became a member of the Organizing Committee of Right Cause coalition and was elected to the Steering Committee of the Organizing Committee of this coalition.

Chubais has received three presidential commendations (awarded in 1995, 1997 and 1998) and as well as one honorary Ph.D. from the St. Petersburg State Engineering and Economic University.

In July 1996, Chubais founded the “Center for Protection of Private Property” Foundation.

In 1997, the British magazine Euromoney named him the world's best Minister of Finance.

In 1998 Chubais was elected to the Chairman of the Board of RAO UES of Russia, the state-owned electricity monopoly, at a special general meeting of shareholders; he soon was also appointed Chairman of the Board.

He was elected President of the CIS Electric Power Council (2000), and later was repeatedly re-elected to that post from 2001 to 2004.

In December 2001, Chubais was awarded an honorary diploma of International Award by the International Union of Economists for his significant contributions to the Russian Federation, specifically his work applying advanced international experience to introduce contemporary methods of organizing administration, economics, finances and production processes.

On 24 January 2004 he resigned from his post as co-chair of the party but remained on the Federal Political Council of the SPS party.

On 17 March 2005 he survived an assassination attempt. Vladimir Kvachkov was charged for the crime, but was acquitted by a jury.

In 2007, the Russian newspaper Vedomosti named Chubais the “Professional of the Year”. The paper called him the only professional reformer in Russia because of his achievements in breaking of one monopoly into dozens of independent entities, introducing market forces into the electricity distribution system, and transforming a government institution structure into one attractive for private investment and management.

In 2008, Chubais was awarded a Presidential Commendation for helping draft part of the Russian Constitution as well as his overall contributions to democracy in Russia

In 2010, Chubais was honored by with IV degree Order For Merit to the Fatherland “for outstanding contribution to the implementation of state policy in the field of nanotechnology and many years of favorable work”.

The official Business of the corporation is to promote innovation and modernization in Russia’s economy in several areas. For Example, RUSNANO forms an important part of the government’s strategy to find economic alternatives in order to reduce the country’s dependence on fossil fuels. Current targets that have been set for the state corporation include reaching 900 billions rubles of sales by the year 2015. In the past, Chubais has compared RUSNANO to a garden, in which the corporation helps to cultivate innovative Business ventures. Over its eight years of operation (2007-2015), RUSNANO has completed over 100 investment projects which resulted in opening of 68 new plants and 28 R&D centers. As stated in the annual RUSNANO groups' financial report, the value of RUSNANO's portfolio is estimated at 227.7 billion rubles and the net income at 17 billion rubles.