The Magpies have long been linked with a move for the Venezuela international, and a deal became a possibility as the Baggies showed an interest in Dwight Gayle.
The pair have now traded places, and both players have acknowledged that they are delighted to have resolved their futures for the upcoming campaign.
Rondon told Newcastle's official website: "It's an honour to be here and I'm excited to get started with my team mates. The clubs were talking for a long time and now I'm focused on the season to help my teammates to get the points to do well this season.
"It's one of the biggest clubs in the Premier League and I knew about the interest of the gaffer, so I'm happy to be here."
Gayle added to West Brom's official website: "The manager (Darren Moore) attracted me. He's really enthusiastic about my game and I'm buzzing to come down and I can't wait to get started."
Rondon could make his Newcastle debut in their Premier League opener with Tottenham Hotspur on Saturday afternoon, while Gayle will hope to feature when West Brom meet Norwich City at the weekend.