Born in 1957 in a rural town in the Netherlands, his earliest influence was the local fanfare orchestra, which included much of his family. Wierbos started out on the cornet and soon switched over to flügelhorn and was asked to join the local band before reaching his teens. Initially trained by the community adult musicians (who had no formal training), Wierbos also received some private lessons. He eventually became first trumpet in Holsten's fanfare, which won first place in a national competition.

Wierbos switched his focus to the trombone when he was 17, because, as he told New Dutch Swing author Kevin Whitehead, the instrument "looked good, and the trombones walk in front" in the town's orchestra. Wierbos took to the instrument and continued to play even after going away to Groningen to study social geography. While there, he first collaborated with pianist Harry de Wit and formed a duo with another trombonist. He was inspired by his first encounter with multiphonics, which he heard in trombonist Albert Mangelsdorff's playing, and upon learning to move his mouthpiece around (to better certain notes) from attending a concert that included trombonist Ray Anderson. Wierbos finally decided to make an attempt at becoming a full-time musician, giving himself five years to do so, before returning to his previous career studies.

Right around 1979, Wierbos joined Cumulus, a group that included de Wit, multi-reedist Ab Baars, tuba player Larry Fishkind, and more. He then got a call from Misha Mengelberg to play in the ICP Orchestra when the band's current trombonist, Radu Malfatti, had a schedule conflict. So, Wierbos went to Amsterdam for to play music. Things happened fast, as Wierbos met saxophonist Sean Bergin (he would later join Bergin's MOB for some recordings beginning in the late '80s, including Kid Mysteries), as well as South African bassist Harry Miller, with whom Wierbos played until Miller's death in 1983 (one album was made of this group, which also included drummer Han Bennink; Down South on the Varajazz label). His first string of gigs with ICP also resulted in an invitation within a year of his arrival in Amsterdam to join Maarten Altena's quartet.

In addition to Wolter Wierbos' continuing participation in the ICP Orchestra over the next two decades, he took part in a number of other groups, including Theo Lovendie's mid-'80s quintet, Paul Termos' tentet, JC Tans and the Rockets, a large group led by Guus Janssen (documented in the late-'80s recording, Dancing Series), Peter van Bergen's LOOS, various dance, film, and theater projects, and Michael Moore's group Available Jelly. Wierbos is most often found performing in groups that also include Ab Baars and/or cellist Ernst Reijseger, with whom Wierbos has performed several hundred concerts. Wierbos is almost always a sideman, but has also performed occasional solo concerts, in addition to recording two solo albums, Wierbos (1982) and X Caliber (circa 1997 on the ICP label). Although he is co-leader of the Podium Trio, these two solo albums are the only recordings attributed to Wolter Wierbos. Nonetheless, his highly respected contributions and experience as a sideman on over 70 recordings led to him winning the most prestigious Dutch jazz award, the Boy Edgar Prijs, in 1995. Among the many other awards presented to the trombonist are the Laren Jazzpodium Prijs and the Podiumprijs for Jazz and Improvised Music.

Although he sometimes plays free jazz, and is completely uninterested in playing wholly composed music, Wierbos seems to prefer, through his choice of projects, a mixture of composition and improvisation, as that heard in ICP Orchestra and in the Gerry Hemingway Quintet (another group he's in). This has led to a wide array of interesting collaborations and guest appearances with bands including Dutch rock band, the Ex, Cecil Taylor's European Big Band, groups led by Butch Morris and Henry Threadgill, and even children's concerts with percussionist Alan "Gunga" Purves and Reijseger. Through his variety of projects, but especially with the ICP Orchestra (still going strong in the year 2000), Wierbos has toured all over Europe and North America and performed in Japan and Indonesia.