He served as Archbishop of Kaunas from 1989 to 1996, and was elevated to the cardinalate in 1988. After studying at the Kaunas Priest Seminary and Theological Faculty in Kaunas, Sladkevičius was ordained to the priesthood on March 25, 1944. He then did pastoral work in Kaišiadorys until 1959, including serving as a professor and the prefect of studies and discipline at the Kaunas seminary.
On November 14, 1957, Sladkevičius was appointed Auxiliary Bishop sedi datus of Kaišiadorys and Titular Bishop of Abora.
He received his episcopal consecration on the following December 25 from Bishop Teofilius Matulionis. However, Bishop Sladkevičius was impeded from performing his ministry by his country"s Communist government, and he took up residence at Nemunėlio Radviliškis, where he was under virtual house arrest from 1963 to 1982.
He was named Apostolic Administrator ad nutum Sanctae Sedis of Kaišiadorys on July 15, 1982, and became President of the Lithuanian Episcopal Conference on April 27, 1988. Pope John Paul II created Sladkevičius Cardinal Priest of Spirito Santo alla Ferratella in the consistory of June 28, 1988, and later Archbishop of Kaunas on March 10, 1989.
In 1993 the Cardinal entered the Congregation of the Marian Clerics of the Immaculate Conception.
He resigned as Kaunas" archbishop on May 4, 1996, after seven years of service. He was awarded the Order of Vytautas the Great in 1998. V. Sladkevičius died in Kaunas, at age 79.
He was buried in the Cathedral-Basilica of Kaunas following a funeral Mass there on June 1, 2000.