Wexler attended Harvard University, and in 1939 he was awarded a Ph.D. in meteorology under Carl-Gustaf Rossby from the Massachusetts Institute of Technology.

He was instrumental in finding funds and support for the measurement and study of carbon dioxide in the atmosphere initiated by Roger Revelle and Charles David Keeling, key work for drawing attention to the problem of global warming.

Wexler had been researching the link connecting chlorine and bromine compounds to the destruction of the stratospheric ozone layers, but died of a heart attack while on vacation in Woods Hole, Massachusetts.

Wexler had already accepted an invitation to deliver a lecture entitled "The Climate of Earth and Its Modifications" at the University of Maryland Space Research and Technology Institute.

Another twelve years would pass before the first papers about the effect of chlorofluorocarbons on the ozone layer were published in 1974, during which CFC production had increased "Had Wexler lived to publish his ideas", author James Rodger Fleming would observe later, "they would certainly have been noticed and could have led to a different outcome and perhaps an earlier coordinated response to the issue of stratospheric ozone depletion.