Kozyrev was born in Brussels in 1951, the son of a Soviet engineer temporarily working there. He was educated at the Moscow State Institute of International Relations, a school for diplomats operated by the Ministry of Foreign Affairs. Before beginning his studies there in 1969, he spent a year as a fitter in the Kommunar machine-building factory in Moscow.
He completed his studies in 1974. He then entered the U.S.S.R. Ministry of Foreign Affairs as a speech writer and researcher in the Department of International Organizations, which was responsible for issues concerning the United Nations and arms control, including biological and chemical warfare issues. Over the next three years, he earned a post-graduate degree in historical science and published several books on the arms trade and the UN.
Kozyrev's career in the Foreign Ministry marked him as a promising young Soviet diplomat. He became an attaché in the Department of International Organizations in 1979 and third secretary the next year. Promotions came regularly: he became second secretary in 1982; first secretary in 1984; counselor in 1986. Following the reorganization of the ministry by Gorbachev's foreign minister, Eduard Shevardnadze, he became deputy chief of the renamed Administration of International Organizations in 1988. The next year Kozyrev became chief of the administration, replacing a man 20 years his senior.
Seizing the opportunity opened by Gorbachev's glasnost in summer 1989, Kozyrev wrote an article repudiating the Leninist concept of the "international class struggle," the very essence of Leninism. Firstly published in the Soviet press, the article was reproduced in the Washington Post and other major news sources all over the world, making him known as a political figure.
In October 1990, a rebellious parliament of the Russian Federation voted to appoint Kozyrev the foreign minister. After the failed Soviet coup attempt of 1991, he found himself in Yeltsin's team of young reformers, which included Yegor Gaidar and Anatoly Chubais, and shared their Western liberal-democratic ideals. He became Russian foreign minister at the age of 39 and gained and kept the confidence of Boris Yeltsin as Russia became an independent state and, in many ways, the successor to the Soviet Union. Kozyrev tried to make Russia a partner with the West in the formation of the post-Cold War world. He emphasized cooperation over conflict with the United States while insisting that Russia be treated as a great power in international politics rather than as a fallen superpower. He favored major arms control agreements with the United States and the nonproliferation of nuclear arms. He was also viewed by many as one of the most important voices for liberalism and democracy in post-communist Russia.
In 1992, Andrei Kozyrev, together with nine other Ministers of Foreign Affairs from the Baltic Sea area, and an EU commissioner, founded the Council of the Baltic Sea States (CBSS) and the EuroFaculty.
In December 1992, Kozyrev underlined his opposition to conservative, nationalistic forces in Russia with a dramatic and unprecedented diplomatic maneuver. He stunned the foreign ministers of the Conference on Security and Cooperation in Europe (CSCE) with a speech that echoed many of the positions of the conservative opposition in Russia and seemed to threaten a return to anti-Western policies. The speech surprised even the Russian delegation. But an hour after giving the speech he retracted it, announcing that the speech was intended to draw attention to the dangers that would come if the opposition took power from President Yeltsin.
At the UN General Assembly Kozyrev declared in 1993, by the time of the end of the Abkhazian War: "Russia realizes that no international organization or group of states can replace our peacekeeping efforts in this specific post-Soviet space."
In the December 1993 elections, Kozyrev ran for a seat in the lower house, the State Duma, as a candidate on the list of the liberal Russia's Choice bloc and as a candidate in the Murmansk region. He took a seat as a representative from Murmansk when the State Duma met in January 1994, having won 60 percent of the vote in a field of 10.
He had been blamed for the international controversy over the conflict in Chechnya. He had also been targeted as a scapegoat for failing to stop North Atlantic Treaty Organization (NATO) bombing of the Bosnian Serbs and of NATO plans to expand into Eastern Europe.
Kozyrev was criticized by the Russian State Duma for capitulating to the West, which led to Russia's loss of the position of "superpower", as well as for the alleged failure to support the Bosnian Serbs during the Bosnian War. He was succeeded by Yevgeny Primakov.
After being elected a second time to the State Duma in Murmansk in January 1996, Kozyrev left the ministry as from now on it was prohibited to occupy both positions. It was a political choice both by him and president. When asked if he had been "sacrificed by Yeltsin ... to pacify anti-reform forces?", Kozyrev told the Los Angeles Times, "of course, there has been some backtracking. Let's face it, there is stagnation. ... It was a genuine political conflict. I lost. I was overruled. I believe that my time will come again, that my policies will be brought back, sooner or later." Since the conclusion of the second Duma term Kozyrev left the government for private business. He now lives in Miami.