Vickrey was born in Victoria, British Columbia and attended high school at Phillips Academy in Andover, Massachusetts. After obtaining his B.S. in Mathematics at Yale University in 1935, he went on to complete his M.A. in 1937 and Ph.D. in 1948 at Columbia University, where he remained for most of his career.
Vickrey married to Cecile Thompson in 1951. He was a Quaker and a member of Scarsdale Friends Meeting. He died in Harrison, New York in 1996 from heart failure.