Veksler was born in Zhitomir on March 4, 1907 in the Russian Empire (now Ukraine) to a Jewish family.

He began working at the Lebedev Physical Institute in 1936, and became involved in particle detector development and the study of cosmic rays.

He participated in a number of expeditions to the Pamir Mountains and to Mount Elbrus, which were devoted to the study of cosmic ray composition.

In 1956 he established and became the first director of the Laboratory of High Energy at the Joint Institute for Nuclear Research in Dubna, where the Synchrophasotron, that, along with Protvino, incorporated the largest circular proton accelerators in the world at their time, was constructed under his leadership.

[6][7] Streets in Dubna, Odesa, Zhytomyr and CERN are named in Veksler's honour.