The 22-year-old midfielder, who will be a member of the Nigeria squad in Russia, has signed a five-year contract after the Potters paid Portuguese side Feirense €7.2million.
Etebo spent the second half of last season on loan with Las Palmas in La Liga and will be heading to England after the World Cup.
Chief Executive Tony Scholes said: “We are delighted Etebo has chosen to join Stoke City, becoming our first signing of the summer.
“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 said: “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 has been capped 14 times by Nigeria and came on as a substitute in last week’s friendly against England at Wembley.
He will be part of the Nigerian squad that will face Group D World Cup games against Argentina, Iceland and Croatia.
Etebo, who started his career with Warri Wolves in his native Nigeria, joined Feirense in 2016 and made 45 league appearances, scoring seven goals. He made 12 appearances for Las Palmas whilst on loan with the team from Gran Canaria.