Brazauskas was born in Rokiškis, Lithuania. He finished Kaišiadorys High School in 1952 and graduated from Kaunas Polytechnic Institute in 1956 with a degree in civil engineering. He later served as a Conscript Sailor in the Soviet Navy, serving as a Fire controlman onboard the Riga-class frigate Rosomacha until 1960 In 1967 Brazauskas started working in the Governmental Planning Committee, as a Committee's head's assistant. In 1974, Brazauskas received PhD in Economics.
He rose to politics in the 1980s, as the Soviet Union was undergoing radical change. In turn he transformed himself from a Communist Party apparatchik to a moderate reformer. He was seen as cautious by nature, and when confronted by the tide of nationalist feeling in the Soviet Union Brazauskas initially believed that the USSR might be reconstituted as a looser federation of independent, but communist, states. In seeing the tide of an independent democracy, he joined the reformist cause observing in 1990 that "We are realists now, and we cannot be propagating any utopian ideas. It's no secret [that] the Communist Party has a dirty history."
Though he sought to avoid a breach with Moscow in 1989, as leader of Lithuania's Communist Party, he formally severed the party's links with Moscow. This was rare in that no other former Soviet republics dared to take this step. Some believe that this act confirmed the inevitability of the demise of the Soviet Union.
In 1988, he became the first secretary of the Communist Party of Lithuania. Under his leadership, the Communist Party of Lithuania supported the Lithuanian independence movement, broke away from the Communist Party of the Soviet Union and transformed itself into social-democratic Democratic Labour Party of Lithuania (now merged into the Lithuanian Social Democratic Party). Brazauskas was Chairman of the Presidium of the Supreme Soviet (head of state) from 15 January until 11 March 1990.
After the 1992 parliamentary elections, he became speaker of the parliament and acting President of Lithuania on 25 November 1992. He then won the presidential election with 60% of the vote, was confirmed as President on 25 February 1993, and served until 25 February 1998. He decided not to seek reelection, and retire, in 1998 and was succeeded by Valdas Adamkus, who won the 1998 election.
He subsequently returned to politics saying he "always had something to do in life." This time he was Prime Minister from 3 July 2001, appointed by the parliament, until 1 June 2006, when his government resigned as President Valdas Adamkus expressed no confidence in two of the Ministers, formerly Labour Party colleagues of Brazauskas, over ethical principles.
He divorced his first wife, Julia, with whom he had two daughters; he married Kristina Butrimienė in 2002.
His government resigned on 31 May 2006 after the large Labour Party left the governing coalition. Brazauskas decided not to remain in office as acting Prime Minister, and announced that he was finally retiring from politics. He said "I tried to be a pensioner for several years, and I think I was successful. I hope for success this time, as well."
He led the ruling Social Democratic Party of Lithuania for one more year, until 19 May 2007, when he passed the reins to Gediminas Kirkilas. He served as the honorary chairman of the party, and remained an influential voice in party politics.
Brazauskas was diagnosed with lymphatic cancer in December 2008. He died on 26 June 2010 from cancer, aged 77. At the time of his death, he was still considered an influential figure in Lithuanian politics.