Studied the saxophone at the Estonian Academy of Music in 1980–85, and in 1989 participated in the Nice International Summer Academy of Music with Professor Claude Delangle. Since 1999 he has taught saxophone and improvisation at Tartu University Viljandi Cultural Academy and run workshops in Germany, Norway, and Nigeria. He is a member of the Board of Estonian Music Festivals.
His repertoire includes classical compositions for alto saxophone and many pieces for saxophone quartet. In the field of jazz, he prefers old swing style, ethno-jazz and funky-groove.
Villu Veski has frequently performed in festivals of Estonian music and at the Contemporary Music Festival NYYD, performing new works by Estonian composers. He has premiered saxophone concertos by Estonian composers Eino Tamberg and Hillar Kareva, both written especially for him. As a soloist he has performed with the Estonian State Symphonic Orchestra, St Petersburg Philharmonic Orchestra, and Tallinn Chamber Orchestra. He is also active in chamber music repertoire and is a member of the Tallinn Saxophone Quartet, who have given concerts both in Estonia and abroad.
The artist has participated in all jazz festivals in Estonia, many Scandinavian ones, including Pori International Jazz (1988, 1999, and 2001), Bergen Nattjazz (1994), Copenhagen European Cultural Capital “Artgenda ’96”, as well as some further afield – the Tbilisi International Jazz Festival (1986), Ossenniye Ritmy Festival in Leningrad (1990), A Step to Parnas in Moscow (1990), and the Adolphe Sax Festival in Dinant, Belgium (1994).
Veski has participated in the recording of eight CDs. An active composer, he has also composed music for TV.