Elouadi received his Bachelor of Science degree from Rabat University (now International University of Rabat) in 1971. A year later he was given a Master of Science and a Doctor of Science degrees from the University of Bordeaux in 1976.
Elouadi began his career as a head of conferences, associate professor in faculty of sciences at Rabat University in 1976. Four years later he took a position of a director of planning and university international relations at Ministry of Education in Rabat and held it for a year.
Brahim worked as a professor of chemistry in faculty of sciences at Rabat University from 1980 to 1990. In 1981, he held the position of a director of Applied Solid State Chemistry Laboratory in Rabat, where he worked until 1988.
He was a visiting professor of chemistry at Oklahoma State University in 1985-1986. Then in 1990 he moved to France and became a professor of chemistry at the University of Paris-Nord. Since 1995 Elouadi has been a professor of chemistry at the University of La Rochelle.
On November 6, 1976 Brahim Elouadi married Françoise Marie Denise Chardac. They have 3 children.