He studied composition with Ton de Leeuw, percussion with Jan Labordus and Jan Pustjens, and piano at the Amsterdam Conservatory of Music.
Meijering has written a large number of compositions (over 700), mainly for small ensembles, which are performed regularly. Many of these works were written for renowned chamber music ensembles such as the Aurelia Saxophone Quartet, the Loeki Stardust Quartet and the Amsterdam Guitar Trio. The end of a specimen (1981) was selected by the Netherlands Ballet Orchestra in a competition for young Dutch composers; Bedouin caravan in the desert (1977) was selected in the Gaudeamus Competition. Referring to his work I can't get no satisfaction (1983), based on the famous song of the Rolling Stones, Meijering states that he considers erotics, sensuality and even obscenity as basic conditions for high-grade performances of his music. These three compositions were used for a ballet by Rudi van Dantzig Want wij weten niet wat wij doen in 1985. He also composed for ballet De neusgaten van Sophia Loren (1986) and Ahnung des Endes (1987). Gedoogzone (1988) for two pianos, was written at the occasion of the 100th anniversary of the Amsterdam Concertgebouw; the violin concerto Neigingen (1986, rev. 1987) was performed by Robert Szreder and the Brabant Orchestra; How to be an Italian for 12 harps and accordion was written for the European Harp Symposium 1995 and P.W. and his skillet lickers (1996) was performed by cellist Pieter Wispelwey and the Amsterdam Sinfonietta. In 1994 he wrote the opera St. Louis Blues (performances in 1995) and in 1998 the opera Gershwin in Blue.