Born in Warsaw in 1954, he studied double bass performance (with Alfred Wieczorek and Andrzej Mysiński) and composition (with Włodzimierz Kotoński) at the Fryderyk Chopin Academy of Music in Warsaw. He continued his composition studies on a 1986 Witold Lutosławski grant with Isang Yun in West Berlin and Klaus Huber in Freiburg im Breisgau (1986–87). As a double bass player, he focuses on the contemporary solo repertoire. He has performed in many European countries, Asia, and the United States. He is also active as an improviser, playing with such ensembles as Mud Cavaliers and Laterna. In 1995 his A Very True Story for tape received the highest prize in the EAR radio competition and Budapest, and in 1999 his Concerto à rebours for violin and orchestra was a recommended work at the International Rostrum of Composers in Paris. 

Wielecki is also active in promotion of contemporary music and arts education. He ran cycles of original radio broadcasts introducing children and teenagers into the world of new music (Something out of Nothing, Sound Graces, Contemporary Music Hits) as well as collaborating with the Children’s Arts Centre in Poznań and the Okopowa Cultural Centre in Warsaw. 

Wielecki was head of the Artistic Committee of the 1992 ISCM World Music Days in Warsaw. In 2004 he was invited as a lecturer to the Darmstadt Summer Courses for New Music. His works have been commissioned by the Darmstadt Courses as well as the Warsaw Autumn, Poznań Philharmonic, Polish Radio and the Polish Radio Symphony Orchestra (POR), Klangspuren Schwaz, Ad Libitum Warsaw, Hiroshima Symphony Association, Klangforum Wien, New Music Orchestra (OMN) in Katowice, Karol Szymanowski Society, Forbidden City Chamber Orchestra in Beijing, Plural Ensemble in Madrid, de ereprijs, Ensemble intercontemporain, Music Workshop, the Silesian String Quartet, Kwartludium, TwoGether Duo, Klangforum Wien, the Polish National Radio Symphony Orchestra (NOSPR), as well as many other ensembles and institutions. 

Tadeusz Wielecki served as director of the Warsaw Autumn International Festival of Contemporary Music between 1999 and 2016. 

Selected works (since 1995): Study of Gesture I for clarinet, piano and cello (1995), Id for large orchestra (1996), Study of Gesture II for piano (1997), Concerto à rebours for violin and orchestra (1998), Thésis for flute (2000), Study of Gesture III for clarinet, trombone, piano, cello and double bass (2000), Credo, quia absurdum for tape and dancer (2001), Time of Stones for double bass and chamber orchestra (2002), Surfaces for symphony orchestra (2002), String Quartet (2004), Whisper of the Semitones for double bass and chamber ensemble (2004), Shoals for symphony orchestra (2005), Necessity and Chance for string quartet and electronic media (2006), The Valley of Dry Water for chamber orchestra (2007), String Vibration for harpsichord (2008), Piano Concerto (2008–9), Knights of the Round Table – A Documentary Opera (2006–9), In the Beginning There Was... for slammer, sampler and chamber ensemble (2009), Quartertones and Half-Shades for double bass, two percussions and trumpet ad libitum (2009), Gear Wheels, Springs and Modes for violin and guitar (2010), Calls for traditional singing, mime and chamber orchestra (2011), The Thread is Spinning... IV for double bass and chamber ensemble (2012), Subjective Model. Dramatised Form for viola, tuba, tape and informal group of performers (2012), Gentle Swaying, dramatic music piece for bass clarinet, violin, tape and informal ensemble (a version of Subjective Model, 2012), Points of Hearing for chamber ensemble (2012), The Little Shoemaker and the False King, chamber opera for children and adults (2013), Reading for orchestra (2014), Dynamistatic Composition for chamber orchestra (2015), A Study of Gesture IV for string trio and percussion (2015), Wobbliness. Dynamistatic Composition II for traditional Chinese instruments (2015), Sphinx for double bass (2015), Multiple Image for chamber ensemble and ticking clocks (2016), Words for piano and ukulele (2016–17), Sound Pranks for sounds, gestures and expressions (2017), I Sound Therefore I Am for accordion and cello (2017), Exercises with Antigone for baritone and percussion (2018), Ungraspability for piano, harp and percussion (2018), Vibrations for accordion and orchestra (2019), There Was Once an Old Man and Woman... for speaking double bassist (2019), Anamnesis for symphony orchestra and electronics (2019), Counting Game, version for speaking double bassist (2020), Continuations for accordion (2020), So to Speak, radio drama for soprano, two actors, chamber orchestra and electronics (2021), Varia for percussion and piano (2023), Poster for ensemble (2023).