He curated exhibitions of works by Claes Oldenburg and Andy Warhol in the 1960s, initiated the Skulptur Projekte Münster in the 1970s, founded the Portikus hall and became a professor at the Städelschule in Frankfurt in the 1980s, and was director of the Museum Ludwig in Cologne from 2000 to 2012.

He established contacts with artists including Carl Andre, Richard Artschwager, Hanne Darboven, Dan Graham, On Kawara, Sol LeWitt, Gordon Matta-Clark, Bruce Nauman, Claes Oldenburg and Andy Warhol.

[6][7] From 1973 to 1975, König taught as an associate professor at the Nova Scotia College of Art and Design in Halifax, Canada.

[4][8][11] Before his death, König donated around 50 works from his art collection to Museum Ludwig,[2] including pieces by Pawel Althamer, Maria Eichhorn, Isa Genzken, Dan Graham, Thomas Hirschhorn, Jenny Holzer, Richard Long and Jeremy Deller.

[12] In 2024, shortly after his death, around 400 works sold from König's private holdings – including works by Richard Artschwager, Thomas Bayrle, William Copley, On Kawara and Sigmar Polke – raised around €6 million ($6.5 million) during a series of sales that took place at the headquarters of Van Ham auction house in Cologne.

[13] Kawara’s May 7, 1967, the sale’s top lot, went for €1.06 million with fees, setting a record for one of the artist’s date-centered works