The 24-year-old has long been linked with a move away from Rosenborg.
Annan is expected to replace Ivan Rakitic at Schalke. Rakitic joined Spanish side Sevilla on Thursday.
“I am happy on Anthony’s behalf. He has been very close to a club change for a while now, so I understand his hunger to move on. We will have a little trouble when he leaves, but we will make do,” Rosenborg coach Jon Joensson told the club’s official website.
