The 22-year-old is seen as a Christian Eriksen replacement, after the Denmark international joined Inter Milan.
Bergwijn was left out of the PSV squad at the weekend, with members of the Dutch accusing the forward of travelling to London without the club’s permission.
But a PSV statement read: “Steven Bergwijn did not join his PSV team-mates for training on Tuesday morning.
“Bergwijn has been given permission by PSV to travel to England to finalise a move.”
Speaking to Dutch newspaper De Telegraaf, Bergwijn explained his excitement at the prospect of playing for Tottenham.
“The Premier League, that is the highest achievable [league] for every football player,” he said.
“Yes, this is certainly a dream come true. It also feels like the right time to take this step.”
The winger also spoke about his admiration for Spurs head coach Mourinho, and experiencing the atmosphere of English football.
“I have always looked up to a top coach like Mourinho. And now I’m going to play for him.
“It’s great to be here. Just look at the facilities around us. When I play on the Playstation Fifa, I almost always choose a team from the Premier League.
“I look forward to playing in that great atmosphere.”