The striker has signed a three-year contract at St James' Park after sealing his move on Wednesday.
"I feel very happy, because I have signed for a very big club," Joselu told Newcastle's official website. "I'm very happy to be part of this club, and so excited.
"I'm looking forward to getting to know my team-mates, the city, the training ground, the stadium and all the supporters."
Joselu spent last season on loan at Deportivo La Coruna in La Liga, scoring five goals in 20 appearances, just nine of which were starts.
That came after he also struggled for regular spot at Stoke, making 22 Premier League outings – only 10 from Mark Hughes' starting XI - after joining from Hannover for €8m in 2015, scoring four times.
The 27-year-old becomes Rafael Benitez's sixth signing of the transfer window after the arrivals of Christian Atsu, Florian Lejeune, Jacob Murphy, Javier Manquillo and Mikel Merino.
"We have known Joselu since his days at the Real Madrid academy, and we know that he has the potential to do well for us," said Benitez.
"Obviously he has experience of English football and the Premier League and that was another thing we took into consideration. We think if we can exploit his full potential he will be a good signing for us.
"He knows and accepts the challenge we've given him at Newcastle United and he's keen to come and fight for a position in the team."
He will hope to make his debut when Newcastle travel to play fellow promoted side Huddersfield Town on Sunday.