Etebo will be a member of the Nigeria squad when the World Cup gets underway in Russia on Thursday.
The 22-year-old is free to concentrate on his international commitments after leaving Portuguese side Feirense in a £6.35 million ($8.5 million) switch to second tier Stoke.
Etebo agreed a five-year contract with Stoke, who were relegated from the Premier League in May and are hoping to win promotion from the Championship next season under new boss Gary Rowett.
"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," Rowett said.
Etebo spent the second half of last season on loan with Las Palmas in La Liga and will link up with his new Stoke team-mates after the World Cup.
He has been capped 14 times by Nigeria and came on as a substitute in last week's friendly defeat against England at Wembley.
Nigeria face Argentina, Iceland and Croatia in the group stage of the World Cup.