Ritchie has agreed a five-year contract at Newcastle and becomes their third signing of the summer.
Reports claim the fee is believed to be between £10m-£15m.
“It’s an unbelievable feeling to come to a football club like this,” said Ritchie.
“I loved it at Bournemouth – I had a fantastic time there and it had a huge impact on my career. But when a club like Newcastle comes calling, I couldn’t pass up this opportunity.”