His awards and honours include an honorary professorship at the Royal Academy of Fine Arts in Copenhagen, Denmark, a professorship at the School of Visual Arts in New York, NY, an honorary professorship at the Royal Academy of Art in London, and an honorary professorship at the Bergen National Academy of the Arts in Norway. He is a member of the Academia Europaea and the Academy of Visual Arts in Vienna. Mollerup has also received the Order of the Dannebrog, Knight First Class.
In 1990, Mollerup became the first professor in the Department of Design at the Copenhagen School of Design and Technology (Hanghals Østufag) in Copenhagen, Denmark. He served as the school's Dean from 1991 to 1998. In 2000 he founded the Department of Design and Interaction Design at the Aalborg School of Architecture, Design and Technology (Aalborg Byggeforskningscenter) in Aalborg, Denmark. Since 2002, he has been a professor of design at the Copenhagen School of Design and Technology, and also held the position of Dean of the School from 2007-2013. From 2004 to 2005, he was a professor of design and interaction design at the School of Visual Arts (SVA) in Copenhagen, Denmark.
Mollerup was professor of design at the Hochschule für Gestaltung in Ulm, University of Applied Arts in Vienna, from 1985 to 1987, and professor of visual communication at the Royal Institute of Art in Stockholm, from 1993 to 1998. He was visiting professor at the Department of Design at the School of Visual Arts at the New York Institute of Technology from 2000 to 2001, and he worked as a lecturer in the Faculty of Humanities and Social Sciences at the Umeå University, Sweden, from 2000 to 2001. Since 2001 he has been a professor of design at the Aalborg University, Denmark. He has also taught at the Royal Academy of Fine Arts in Copenhagen, Denmark, since 1991. In 1996, he received the Danish Design Award for Lifetime Achievement.