Van Kampen was born to Dutch parents in Belgium, where his father had recently taken a job as an accountant in Antwerp.

At the age of 16 he graduated from high school and entered Leiden University to study mathematics.

[1] In 1931, Van Kampen took up the position which he had been offered at Johns Hopkins University in Baltimore, Maryland, and travelled to the United States.

There he met Oscar Zariski who had taught at Johns Hopkins as a Johnston Scholar from 1927 until 1929, when he had joined the Faculty.

[1] By the late 1930s, Van Kampen started to suffer from headaches which in 1941 were diagnosed to arise from a tumor originating from a birth mark near his ear.