Born in Moscow, his Father, professor of computer science Oleg Aven (Russian: Олег Иванович Авен), was half Latvian and half Russian and his mother was from a Jewish family. His paternal grandfather Janis Aven or Jānis Avens (lv) was a Latvian rifleman. Petr Aven graduated from Moscow State University in 1977 and holds a PhD in Economics (1980). Subsequently, Petr was a senior researcher at the All-Union Institute for Systems Studies at the USSR Academy of Sciences and then spent time at the International Institute for Applied Systems Analysis in Laxenburg, Austria (1989–1991).

Concerning Russian economic reform in the early 1990s, he and other reformer colleagues had consulted with foreign academics by 1990 on trying to find a new system. When Boris Yeltsin became President, he appointed Aven with the task of making the ruble convertible and finding a solution to foreign debt. Aven went on to become the Minister of Foreign Economic Relations for the Russian Federation (1991–1992), serving as Russia's representative to the Group of Seven and conducting a number of high-level trade and economic missions to Western capitals. In 1993 he joined the Russia's Choice movement and was a candidate for State Duma.

Aven is also a recognised art collector. His first art purchase was a still life by Pavel Kuznetsov in 1993, and afterwards he began collecting mostly pre-Soviet Russian art, as well as art by artists of other nationalities. Works from his collection have been lent to the Jewish Museum in Moscow, the Tate in London, the Museum of Modern Art in New York and recently the Royal Academy. In May 2015, pieces from Aven’s private collection were put on display at New York’s Neue Galerie in an exhibition examining early twentieth century Russian art and its relationship with German art of the time.

In October 1994, Aven met Alfa Group's Mikhail Fridman, and soon became an Alfa Bank shareholder serving as a member of the Supervisory Board of the Alfa Group Consortium. From 1994 until June 2011, he served as the President of Alfa-Bank Russia. Currently Aven is a Member of the Board of Directors and Chairman of the Board of Directors of ABH Holdings S.A. Aven is also Chairman of the Board of Directors at AlfaStrakhovanie Group, Co-Chairman of the Board of Directors of CTC Media, Inc. In 2012, the Alfa Group together with Viktor Vekselberg of Renova Group and Leonard Blavatnik of Access Industries sold their aggregate 50% stake in TNK-BP to state-owned Rosneft for $28 billion. In 2013, Aven joined the Board of LetterOne Group, an international investment Business founded by Mikhail Fridman and focused on the telecoms, Technology and Energy sectors. The L1 Group owns companies – and has equity Investments in companies – with operations in 32 countries around the world.

He has received a number of international awards, including the best manager in the financial services sector in Russia in 2004 by Institutional Investor.

Since April 2006, Petr Aven has been a member of the Board of Directors of the Russian Union of Industrialists and Entrepreneurs.

In 2007, Mr. Aven became Chairman of the Russia-Latvian Business Council.

On 3 November 2015, Petr Aven received the Woodrow Wilson Award for Corporate Citizenship in recognition of his contribution to corporate and public Service to U.S.-Russia relations, at the 2015 Kathryn and Shelby Cullom Davis Awards Dinner. The award was given to Mr Aven in recognition of his many achievements in building understanding between Russians and Americans during his career.

In May 2017 Aven, along with fellow Alfa-Bank owners Mikhail Fridman and German Khan, filed a defamation lawsuit against BuzzFeed for publishing the unverified Donald Trump–Russia dossier, which alleges financial ties and collusion between Putin, Trump, and the three bank owners.