We study the effects of welfare generosity on international migra- tion using reforms of immigrant welfare benefits in Denmark. The first reform, implemented in 2002, lowered benefits for non-EU immigrants by about 50 percent, with no changes for natives or EU immigrants. The policy was later repealed and reintroduced. Based on a quasi-experimental research design, we find sizable 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 evi- dence on the welfare magnet hypothesis.