The midfielder's existing deal was set to expire in 2016, but the new contract sees the playmaker extend his stay at the Amsterdam ArenA by an additional two seasons.
Having broken into the first-team picture this season, Klaassen has made 22 appearances in the Eredivisie and contributed a healthy return of nine goals as Ajax bid for a fourth successive league title.
Speaking to the club's official website, the 21-year-old said: "This is a logical step for me. We really want to start building something with Ajax, and I think we are doing well.
"I believe that beautiful things can happen."
Klaassen made his debut for Ajax in November 2011 against Olympique Lyonnais in the Champions League.
Ajax can secure the title with victory at Vitesse on Sunday, providing Feyenoord fail to beat RKC Waalwijk.