After graduation from Baton Rouge High School, McGehee matriculated at Rice University, where he received his B.A.
His doctoral dissertation was Two Problems of Fourier Analysis on Thin Sets, supervised by Yitzhak Katznelson.
[2] At the University of California, Berkeley, McGehee was an instructor from 1965 to 1967 and an assistant professor from 1967 to 1971.
At LSU he was chair of the mathematics department from 1979 to 1984 and dean of the division of academic services from 1986 to 1990.
[1] In 1967–1968 he was a NATO Postdoctoral Fellow at the Faculté des Science d'Orsay, France.