Andrzej Rudolf Zaucha was born on January 12, 1949 in Kraków and grew up in the city's Pychowice district. His father, Roman, drummed and sang in bands that played at parties and dances, and at eight Andrzej made his first public appearance by sitting in for him on the drums. He never studied music and never took a singing lesson. As a teenager he was a serious canoeist, winning junior national titles in the singles and fours in 1964 and being considered for the Polish squad for the Tokyo Olympics that year, before he dropped sport to play drums in a Kraków band called Czarty. He left secondary school in his final year and trained as a typesetter.

He sang for the first time in student clubs in 1966; enthralled by the records of Ray Charles, he changed the way he used his voice. In early 1969 the bassist Marian Pawlik and the drummer Benedykt Radecki, who had heard him perform at the Polfa club, took him on as lead singer of their jazz-rock group Dżamble, which was linked to the city's Helikon jazz club. That year Dżamble won a special award at the Jazz nad Odrą festival in Wrocław, with an individual prize for Zaucha, and he won first prize at the Student Song Festival in Kraków; the band was named discovery of the year for 1969 in a poll run by the monthly Jazz. In 1970 the group appeared at the Lublin meetings of jazz vocalists, spent a week at Zofia Komeda's Casino Jazz at Night in Sopot, and played the twelfth Jazz Jamboree in Warsaw and the Zaduszki Jazzowe in Kraków.

The band's one album, Wołanie o słońce nad światem (Polskie Nagrania Muza), was recorded in February 1971 with leading Polish jazz players as guests: Tomasz Stańko on trumpet, Janusz Muniak on flute and saxophones, Zbigniew Seifert on saxophone, and Michał Urbaniak on saxophones and electric violin. Zaucha wrote part of the music, including "Naga rzeka," the first song he composed. When Dżamble broke up in May 1972 he joined Anawa, the Kraków group led by the pianist Jan Kanty Pawluśkiewicz, which mixed poetry with avant-garde and jazz-rock arrangements and took part in the cultural programme around the 1972 Munich Olympics. The group's only record with him, Anawa, appeared in 1973.

Soon after it he left Anawa to concentrate on playing, and the following years were his most jazz-oriented. He sang and played with the Kraków traditional-jazz band Old Metropolitan Band, touring Poland and giving a series of concerts in Hanover before leaving it in 1984, and Polish Wikipedia lists the traditional-jazz groups Beale Street Band and Playing Family among his collaborators as well. Between 1973 and 1979 he worked in clubs and pubs in West Germany, Austria, Switzerland and the Netherlands, and from 1976 he played tenor saxophone. At the end of 1978 he revived Dżamble, which cut singles for Tonpress in 1979, recorded material by other artists including Maanam and Maryla Rodowicz, and stopped working in 1981.

His solo career began in 1980 with the song-play Pozłacany warkocz by Katarzyna Gärtner, a single on Tonpress, and blues recordings with the band Kasa Chorych. The first solo album, Wszystkie stworzenia duże i małe (Polskie Nagrania Muza, 1983), carried a popular title duet with Ewa Bem and had the jazz saxophonist Henryk Miśkiewicz among its players. He sang at the National Festival of Polish Song in Opole in 1985 and returned most years afterwards, released Stare, nowe, najnowsze (Wifon, 1987), built mostly from Polish Radio recordings of 1980 to 1986, with "Bądź moim natchnieniem" and "C'est la vie (Paryż z pocztówki)," and won a distinction at Opole in 1988 for "Byłaś serca biciem," one of his biggest hits. He also sang the title music for the television series Przybysze z Matplanety and, in 1990, the theme of the Polish version of Gummi Bears, and played small parts in the films Misja specjalna (1987) and Trzy dni bez wyroku (1991).

The jazz side of the 1980s peaked in 1989, the year he marked twenty years as a vocalist. His album Andrzej Zaucha (Polskie Nagrania Muza, SX 2565) was recorded with the big band of the jazz arranger and bandleader Wiesław Pieregorólka, who had also composed "C'est la vie (Paryż z pocztówki)" for the 1987 record, and its songs have English lyrics. At Opole that year he received a distinction for "O cudzie w tancbudzie" and the city of Opole's prize for achievement in song performance. His wife, Elżbieta Witkowska, whom he had known since 1966, passed away on August 31, 1989, at 39. In the early 1990s he toured Poland in a cabaret and music programme with Andrzej Sikorowski and Krzysztof Piasecki, and in 1990 and 1991 he played the title role in the musical Pan Twardowski at Teatr STU in Kraków, directed by Krzysztof Jasiński.

On October 10, 1991, after a performance of Pan Twardowski, he and the actress Zuzanna Leśniak walked to a car parked on ulica Włóczków. Her husband, the French director Yves Goulais, opened fire; Zaucha was killed on the spot, and Leśniak died in hospital afterwards. Goulais was convicted and sentenced to fifteen years in prison. Zaucha was 42. He was buried on October 16 beside his wife in Kraków's Batowice Cemetery, with several thousand mourners present. The album Ostatnia płyta followed in 1992, with music by Jerzy Dobrzyński and words by Zbigniew Książek, and since 2009 an annual festival, Serca Bicie, has been dedicated to his memory. A star for him was unveiled on the Opole Walk of Fame on June 14, 2015, and his songs are still sampled, with "Byłaś serca biciem" reworked by the rapper Taco Hemingway in 2025.

Zaucha was a Polish rhythm and blues and pop-jazz singer, and most of his catalogue is exactly that: songs in Polish for the pop, festival and television audience, together with film and cartoon themes, a cabaret programme and a leading role in a stage musical. Jazz was where he learned the trade rather than where he stayed. The traditional-jazz bands, the jazz club where Dżamble was based, his drumming and later his tenor saxophone were his schooling, and his first album was recorded with leading Polish jazz soloists as guests. His vocal style came from rhythm and blues: enthralled by the music of Ray Charles, he changed the way he sang in the mid-1960s.

His jazz-related recordings are few and mostly early: the Dżamble album of 1971, the Anawa album of 1973 and the 1989 big-band record with Wiesław Pieregorólka. The rest is Polish pop and rhythm and blues, and the Jazz Pop and Jazz Rock tags describe those parts of his career rather than a body of straight-ahead jazz. In Poland he is remembered above all for his songs, for the festival and Opole star dedicated to him, and for the way his career ended; his recordings have since been sampled by Polish rappers including Taco Hemingway and PRO8L3M, and Kuba Badach recorded a tribute album of his songs in 2009.