We study the effects of welfare generosity on international migration using reforms of im- migrant welfare benefits in Denmark. The first reform, implemented in 2002, lowered benefits for non-EU immigrants by about 50%, with no changes for natives or EU immigrants. The pol- icy was later repealed and re-introduced. Based on a quasi-experimental research design, we find sizeable effects: the benefit reduction reduced the net flow of immigrants by about 5,000 people per year, and the subsequent repeal of the policy reversed the effect almost exactly. The implied elasticity of migration with respect to benefits equals 1.3. This represents some of the first causal evidence on the welfare magnet hypothesis.