The Germany striker scored the winner in victory over Wolves on Saturday.
Woltemade told Sky Deutschland: The Newcastle project is really cool. The coach and the core of the team have been here for years. I've been to two incredible clubs with really great fans in Bremen and Stuttgart.
"Here in Newcastle, the fan culture is completely different, but it's also a huge club! I can already feel that. Everyone here is passionate about this club. That's something that really appeals to me."
Woltemade cites qualification for the Champions League and the League Cup win as reasons to be excited: "Last year, the club finally won a title again after 70 years. That's the path we should continue on now. I'm up for the task, I'm up for the challenge. That's why I'm here."
Woltemade joined Newcastle for €75m and he continued: "Even though I have the price now, it still doesn't change anything for me to say I'm taking my time. That's important. Ultimately, I try not to look at the numbers. For me, performance counts, and I don't want to link that with money. If outsiders do that, that's just the way it is; it's the business and part of it.
"It's a different level here, a different intensity. You have to get used to it. And once I've gotten used to it, you'll see why I'm here."