The 22-year-old has signed a one-year contract extension, with the club he joined in the summer of 2007.
The new deal will keep Suarez at the club until 2013.
“Everyone was speculating about a transfer, but I was negotiating with Ajax about the extension of my contract,” he said.
“Ajax is a fantastic club and this team can grow further.
“I enjoy living in Amsterdam and the team is still developing. The signing of (Nicolas) Lodeiro won me over.”
