Brinkman was born in Rotterdam, Netherlands, in 1902.[3] He was the son of architect Michiel Brinkman (1873–1925), who established a firm in Rotterdam in 1910 and was known for designing the Spangen neighborhood of Rotterdam in 1922. Johannes studied civil engineering at the Delft University of Technology (Dutch: Technische Universiteit Delft). After Michiel's death in 1925, Johannes took charge of the father's architectural firm and entered into a partnership with architect Leendert van der Vlugt. The results of that collaboration include the Van Nelle Factory and the Feijenoord Stadion.[2]
Brinkman died in 1949 and the architect Jaap Bakema joined the firm, which in 1951 was renamed Architectenbureau Van den Broek en Bakema and today is known an Broekbakema.[2]