He graduated from secondary school in Seirijai in 1955 and entered the Kaunas Priest Seminary. He spent several years in the military service in the Soviet Army and then continued his theology studies, graduating from the seminary in 1962. He was ordained priest by Bishop Petras Maželis on 18 April 1962. He ministered as vicar in the parishes of Alytus, Lazdijai, Kudirkos Naumiestis, Prienai, Simnas. In 1968 he entered the Society of Jesus, which was then illegal under Soviet law. Tamkevičius was among the initiators of the petition action protesting the Soviet discriminating restrictions on the Kaunas Seminary. Because of that Soviet authorities forbade Tamkevičius from exercising his ministry. He worked in a factory and in the land-reclamation area for one year. While vicar in Simnas parish, Tamkevičius initiated the underground publication of the Chronicle of the Catholic Church of Lithuania in 1972. The Chronicle registered and made public in the West the facts of religious discrimination in Soviet Lithuania. The underground publications were persecuted by KGB. Tamkevičius was the pastor of Kybartai parish from 1975 until 1983. At the same time he was the editor of The Chronicle for 11 years until his arrest in 1983. Tamkevičius together with four other Lithuanian priests founded the Catholic Committee for Defense of the Believers’ Rights in 1978. Tamkevičius was arrested and put under trial, being accused for alleged anti-Soviet propaganda and agitation in 1983. He was sentenced with ten years term of the prison and exile. Tamkevičius spent his prison term in the labor camps of Perm and Mordovia. He was exiled to Siberia in 1988. With the liberalization of Soviet politics under perestroika, he was released. The Lithuanian Bishops' Conference appointed Tamkevičius spiritual director of the Kaunas Seminary in 1989. He was appointed rector of the Seminary in 1990. Tamkevičius was appointed auxiliary bishop of Kaunas on 8 May 1991 and was consecrated a bishop on 19 May 1991. Pope John Paul II appointed him Archbishop of Kaunas on 4 May 1996. Within the Lithuanian Episcopal Conference, he has been President and Vice-President. Pope Francis accepted his resignation on 11 June 2015. On 5 October 2019, Pope Francis made him Cardinal Priest of Sant'Angela Merici.
