He is a professor in the Institute for Theoretical Computer Science at ETH Zurich in Switzerland.

He studied at the Graz University of Technology receiving a Diplom in Applied Mathematics in 1981 and a doctorate in 1983 under the supervision of Hermann Maurer.

[1] Welzl is a member of multiple journal editorial boards, and has been program chair for the Symposium on Computational Geometry in 1995, one of the tracks of the International Colloquium on Automata, Languages and Programming in 2000, and one of the tracks of the European Symposium on Algorithms in 2007.

With David Haussler, he showed that machinery from computational learning theory including ε-nets and VC dimension could be useful in geometric problems such as the development of space-efficient range searching data structures.

[6] Other highly cited research publications by Welzl and his co-authors describe algorithms for constructing visibility graphs and using them to find shortest paths among obstacles in the plane,[7] test whether two point sets can be mapped to each other by a combination of a geometric transformation and a small perturbation,[8] and pioneer the use of space-filling curves for range query data structures.