Klonowski was born in Moscow, where his parents briefly lived at the end of World War II, on their way back from a Bashkir village in the Ural Mountains, where they had been displaced after the Soviet invasion of Poland in September 1939.

Then he worked for several years at the Institute of Basic Technological Research Polish Academy of Sciences on theory of networks and of sol-gel transitions in macromolecular systems.

He was a fellow at the Max Planck Institute of Biophysical Chemistry in Goettingen, Germany (1982–1984) and then with German Fremdenpass, because Polish People Republic refused to give him a valid passport, he moved as a visiting professor to Brandeis University, Waltham, MA, USA (1984–1986).

In 1986 Klonowski decided to emigrate officially to Canada where he has worked at McMaster University, Hamilton, Ontario, and then moved to Halifax, NS, where he established a small computer consulting and tutoring firm.

While working in Göttingen Klonowski wrote his habilitation thesis on the theory formation of supramolecular structures in (bio)polymer systems and submitted it to Humboldt University, Berlin (then DDR), since it was recognized in the West as being German and in the East as being socialistic.

Klonowski returned to Poland at the end of 1994 and in 1995 he joined the Institute of Biocybernetics and Biomedical Engineering Polish Academy of Sciences where he served as the Head of the Laboratory of Biosignal Analysis Fundamentals.

He served as the editor of series Frontiers of Nonlinear Dynamics (Pabst Science Publisher, Lengerich, Berlin: Attractors, Signals, and Synergetics (2002); From Quanta to Societies (2003), Simplicity behind Complexity (2004)).

In FP 6. he sat on physics panels as an individual expert for Marie Curie and NEST Actions of the European Community and served as the leader of the Group of Biosignal Analysis Fundamentals (GBAF, Medical Research Center Polish Academy of Sciences) in IST Integrated Project SENSATION (2004–2007).