Born in 1954 in Warsaw, he studied composition with Włodzimierz Kotoński and double bass with Alfred Wieczorek and Andrzej Mysiński at the Warsaw Academy of Music. In 1986 he was granted a Witold Lutosławski scholarship to continue his composition studies with Isang Yun in West Berlin and Klaus Huber in Freiburg im Breisgau (1986–87). As a double bass player, he has given concerts in many European countries, as well as in Asia and the United States, where he has presented contemporary solo repertoire. He also plays improvised music with the ensembles Mud Cavaliers and Laterna. In 1995, his The Very True Story for tape won the 2nd Prize (1st Prize not awarded) in the EAR radio competition in Budapest, and in 1999 Concerto à rebours for violin and orchestra was recommended at the International Rostrum of Composers in Paris. Tadeusz Wielecki is also involved in the promotion of contemporary music and artistic education. He has hosted original broadcasts for children and teenagers (Something Out of Nothing, Sonic Grace, and Hits of Contemporary Music) on Polish Radio. He has cooperated with the Children’s Art Centre of Poznań and the Association for Culture and Education in Warsaw. He chaired the Artistic Committee of the ISCM World Music Days held in 1992 in Warsaw. In 2004 he was invited as a lecturer to the International Summer Courses for New Music in Darmstadt. 

He has received commissions from the festivals and institutions including the Darmstadt courses, Warsaw Autumn, Poznań Philharmonic, Polish Radio and Polish Radio Orchestra, Klangspuren in Schwaz, Ad Libitum in Warsaw, Hiroshima Symphony Orchestra, Klangforum Wien, New Music Orchestra in Katowice, Szymanowski Society, Forbidden City Chamber Orchestra, Plural Ensemble, orkest de ereprijs, Ensemble intercontemporain, Music Workshop, Silesian String Quartet, Kwartludium, TwoGether Duo, Polish National Radio Symphony Orchestra, and many others. 

In the years 1999–2016, Tadeusz Wielecki was the director of the Warsaw Autumn Festival. 

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 Waters 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 percussion and trumpet ad libitum (2009), Gear Wheels, Springs and Modes for violin and guitar (2010), Callsfor traditional singing, mime and chamber orchestra (2011), The read 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 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).