The first modern welfare state is commonly understood to be Germany, which developed Staatssozialismus under Chancellor Otto von Bismarck in the late 19th century. In 1881 the Reichstag approved Bismarck's proposed welfare legislation, introducing health insurance, disability insurance, worker's compensation, and a pension system.

Interestingly, Bismarck introduced this program in large part to combat the popularity of socialism among the working class. This explains Bismarck's reversal from his opposition to such policies earlier in his career: a staunch anti-socialist, he feared that social inequities would lead to a collapse of the system already in place and allow socialist ideas to flourish.

I am using Bismarck by AJP Taylor as a source, though the US Social Security Administration has a neat little write-up.