The 24-year-old completed a medical at the Dutch champions on Wednesday before signing the deal, which is worth €31.25 million -- an Eredivisie record.
The move marks a return to the Eredivise for Bergwijn, who lifted the Dutch title three times with PSV Eindhoven before making a €35m switch to Spurs in January 2019.
Bergwijn scored eight goals in 83 games for Spurs in all competitions, playing under three managers -- Jose Mourinho, Nuno Espirito Santo and Antonio Conte.
The Netherlands international joins Ajax amid a turnover at the club. Striker Sebastien Haller has joined Borussia Dortmund in a €36m deal, while midfielder Ryan Gravenberch left the club for Bayern Munich. Head coach Erik ten Hag also left this summer to join Manchester United and has been replaced by Alfred Schreuder.
On Bergwijn's move, Schreuder said: "It is indicative of Steven's ambition that he chooses to make the step to Ajax. He is a player with many qualities, has an enormous drive and is also very goal-oriented.
"Of course I am happy that we were able to capture him, it means a new quality for our selection."
Meanwhile, defender Lisandro Martinez is attracting interest from Premier League giants Arsenal and United. The 24-year-old, who can play in midfield or defence, is valued at around £43m but Ajax have signalled they may be willing to compromise over the fee.
Arsenal have had two bids knocked back for Martinez giving United the opportunity to work towards their own agreement. Old Trafford bosses have also enquired about signing winger Antony but Ajax have so far stuck to their valuation of £70m and United would not be interested in that price.