Hoffenheim, who needed a relegation play-off against second division Kaiserslautern in May to secure their top flight status for next season, have agreed a three-year deal with the player until 2017. No financial details were released.
"Tarik is very skilled, fit and can be deployed in attack in a number of positions," Hoffenheim first team director Alexander Rosen said in a statement on Monday. "He fits our idea of football and we are delighted to have succeeded in signing him."
Moroccan-born Elyounoussi, who joins from Rosenborg Trondheim, has won 21 caps for Norway.