In 1977, Alexander Lebedev entered the Department of Economics at Moscow State Institute of International Relations. After he graduated in 1982, Lebedev started work at the Institute of Economics of the World Socialist System doing research for his Kandidat (between master's degree and doctorate) dissertation, The problems of debt and the challenges of globalization. However, he soon transferred to the First Chief Directorate (Foreign Intelligence) of KGB. He worked there and at its successor Foreign Intelligence Service until 1992. In London, Lebedev had the diplomatic cover of an economics attaché. According to his personal website, Lebedev's assignments included fighting capital FLIGHT from the Russian Federation. The Sunday Express stated that he "spent more time studying Finance and the City than British secrets".

Upon leaving the Russian intelligence community, Lebedev set up his first company, the Russian Investment-Finance Company. In 1995 this bought the National Reserve Bank, a small Russian bank which was in trouble at the time. The bank subsequently grew rapidly to become one of Russia's largest banks. It and the Alfa-Bank were the only two out of the ten biggest Russian banks to survive the 1998 Russian financial crisis. Among the bank's assets are:

Lebedev's first wife was Natalia Vladimirovna Sokolova, daughter of the scientist Vladimir Sokolov, with whom he has one child, Evgeny Lebedev. They separated in 1998.

In 2003, Lebedev stood as a candidate for elections to the Mayoralty of Moscow and the State Duma. He received 13% in the Mayoral elections, losing to Yuriy Luzhkov, but won a seat in the State Duma on the Rodina party list (he was actually number one on the Moscow regional list of the party). He remained in the Duma until 2007, when new elections were held. In the Duma, he initially moved from nationalist Rodina to the pro-Government United Russia fraction, but after Rodina was merged into the larger social-democratic coalition Fair Russia, he made his return.

In September 2008, Russian Politician Mikhail Gorbachev announced he was going to make a comeback to Russian politics along with Lebedev. Their party was called the Independent Democratic Party of Russia.

In March 2009, Lebedev announced that he would be running for mayor of Sochi, host of the 2014 Winter Olympics, but a court ruling declared his candidacy invalid on 13 April 2009. The court ruling was a result of a complaint by another candidate, Vladimir Turukhanovsky, that Lebedev's campaign received three donations from minors that is forbidden by Russian electoral law. According to the chief of Lebedev's electoral campaign, Artyom Artyomov, the three teenagers were led to Sberbank by a staff member of the Sochi council, given 500 rubles each (approximately $20), and told to donate the money to Lebedev's campaign. His campaigners sent the money back the same day, it was received but still it was found sufficient to disqualify his candidacy. Lebedev said that he intended to appeal the court's decision.

In 2009 he entered into exclusive negotiations with Independent News & Media to buy the company's British national newspapers, The Independent and Independent on Sunday. Before the purchase was completed, his representatives offered the editorship of The Independent to Rod Liddle, former Editor of BBC Radio 4's Today Programme. The offer was withdrawn after Liddle became the subject of a campaign of hostility online and from the newspaper's staff. On 25 March 2010, Lebedev bought The Independent and Independent on Sunday for £1.

In September 2011 while appearing on a Russian television programme, he punched a fellow guest, Billionaire property developer Sergei Polonsky (Сергей Юрьевич Полонский). Lebedev claimed afterwards that he had reacted to Polonsky's threat of violence towards him. Lebedev was later charged with hooliganism and sentenced to community Service for that incident.

On 5 November 2012, Lebedev announced he would close all the regional offices of the National Reserve Bank and sell off the real estate as well as 75% of the bank's loan portfolio, worth 16.8bn rubles ($542m). Also in November 2012, Lebedev announced that he is selling off his assets in Russia.

Alexander Lebedev was born in Moscow. His parents were part of the Moscow intelligentsia. His Father, Yevgeny Nikolaevich Lebedev, was an elite athlete–a member of the Soviet national water polo team, and later a professor at the Bauman Moscow State Technical University, Moscow's highest technical school. After graduating from Moscow Pedagogic Institute, Alexander's mother, Maria Sergeyevna, worked in a rural Sakhalin school and later taught English in a Moscow tertiary school.