Joselu impressed during the Potters' pre-season fixtures, scoring four goals, but it has been a difficult two years at the bet365 Stadium.
In his first season at Stoke, the forward managed just four goals and in the following campaign he was sent out on loan to Deportivo La Coruna, where he found the back of the net four times in 20 appearances.
Now, Joselu, who had a brief stint at Real Madrid in 2011, has opted to take on a new challenge at St James' Park.
"I feel very happy, because I have signed for a very big club. I'm very happy to be part of this club, and so excited," the 27-year-old told the club's official website.
"I'm looking forward to getting to know my teammates, the city, the training ground, the stadium and all the supporters. I'm very happy to be here."
Benitez added: "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. 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."
The Magpies kicked off their Premier League campaign with a 2-0 defeat to Tottenham Hotspur last weekend.