The 24-year-old has penned a four-year deal, keeping him at his new club until at least June 2018.
Joselu spent last season on loan at Eintracht Frankfurt, scoring 14 goals in 33 appearances across all competitions.
And the Spaniard is thrilled to have made the switch to Tayfun Korkut's side.
"My goal was to move to a club with a clear outlook for me," he told the club's official website. "I join a great team and a very ambitious manager at Hannover.
"The talks with (president) Martin Kind, (sporting director) Dirk Dufner and Tayfun Korkut convinced me that I can take the next step here and that I fit perfectly with the team and the playing philosophy.
"I will be part of a team that like to play attractive football and are hungry for success. I want to repay my delight with goals and I'm already looking forward to pre-season and my first matchday in a Hannover kit."
Joselu started his career with Celta Vigo in his homeland, before joining La Liga giants Real Madrid.
He then moved on to Hoffenheim in August 2012, registering five goals in 25 appearances during his first season at the club.
