Krabbé was born in Amsterdam. His writing has appeared in most major periodicals in the Netherlands. He is known to Dutch readers for his novel De Renner (The Rider), first published in 1978 and translated into English in 2002, of which The Guardian's Matt Seaton wrote: "Nothing better is ever likely to be written on the subjective experience of cycle-racing". English readers know him primarily for The Vanishing, the translation of his 1984 novel Het Gouden Ei (The Golden Egg), which was made into an acclaimed 1988 Dutch film for which Krabbé co-wrote a script. A poorly received American remake was made in 1993. In 1997 he published 'De grot', translated as 'The Cave' and published in the U.S.in 2000. In 2009, he wrote the "Boekenweekgeschenk", called Een Tafel vol Vlinders.
Also a former championship chess player, Krabbé is renowned for his writings on the subject and maintains a chess website. Krabbé once authored a chess puzzle which featured a rook castling vertically (see joke chess problem), before this move was specifically disallowed. His FIDErating is 2274..