Meyerstein was born in Jerusalem in Mandatory Palestine. He earned a M.Sc. from The Hebrew University of Jerusalem in Physical Chemistry (1961), and a Ph.D. in Chemistry from the school as well (1965).
Meyerstein is Professor Emeritus of Ben-Gurion University of the Negev a member of the Academia Europaea, the American Chemical Society, and the Royal Society of Chemistry.
In 2004, Meyerstein opened the third annual David Bar-Illan Conference on the Media. Concerning the demographics of Israel, Meyerstein has stated that the birthrate in the Judea and Samaria District is "crazily higher than the rest of Israel."