The 22-year-old scored 10 times for the Canaries last season and was one of the standout performers for England at this summer's Under-21 European Championship in Poland.
Murphy passed a medical in Dublin on Tuesday ahead of joining his new teammates on Wednesday following a transfer thought to have cost the Magpies an initial fee of £10m.
"It was a childhood dream of mine to represent Newcastle and the opportunity is now here. I can't wait to get started," Murphy told the official Newcastle website.
Toon boss Rafael Benitez added: "He's a young and talented player and hopefully he can develop even more here. We hope he can show us the passion, commitment and ability that he showed in the Championship last season."