Olfert Dapper was born in 1635 or possibly early 1636 in Amsterdam in the Dutch Republic. In January 1636, he was baptized in the Lutheran church in Amsterdam.

In 1658, he registered at the University of Utrecht. After two years, he was signing himself as doctor medicinæ, but there is no evidence that he studied medicine.

He wrote a book on the history of Amsterdam. Later he also wrote about Africa, China, India, Persia, Georgia, and Arabia, although he had not visited these exotic destinations himself. In fact, he never travelled outside Holland. His books became well-known in his own time. Translations appeared in English, French, and German.

He died on 29 December 1689 in Amsterdam.

To this day, Dapper's book Description of Africa (1668) is a key text for Africanists.

In Amsterdam, the street Dapperstraat was named after him.

In Paris, the Musée Dapper was opened in 1986, named after Dapper. The Dutch writer Willem Frederik Hermans visited the museum and wrote a book on it with the title Het Evangelie van O. Dapper Dapper (1973).

Peter S. Beagle dedicated The Last Unicorn to Dr. Dapper for his reports of unicorns in Maine.