The World Cup-bound Nigeria international joins the Potters on a five-year deal ahead of their first campaign back in the Championship.
Stoke have paid €7.2m (£6.3m) to sign the 22-year-old, who spent the second half of last season on loan with Las Palmas in La Liga.
"We are delighted Etebo has chosen to join Stoke City, becoming our first signing of the summer," Scholes told Stoke's official website.
"I'm particularly pleased that he took the time to look beyond our current league status and understand who we are as a club before choosing us ahead of current Premier League and Bundesliga clubs."
Manager Gary Rowett added: "We're really excited to have got the deal over the line for Etebo. I'm looking forward to seeing him in a Stoke City shirt as I'm sure our supporters are too.
Etebo earned the 13th of his 14 Nigeria caps in the recent friendly defeat to England at Wembley Stadium.