The Italy international is expected to undergo a medical on Thursday before putting pen to paper on a six-year contract.
The move will make Tonali Tottenham's club-record signing and their sixth arrival of a busy summer transfer window.
He joins Mateus Fernandes, Jan Paul van Hecke, Marcos Senesi, Andy Robertson and Martin Dubravka in signing for Roberto De Zerbi this summer, bringing an end to his three-year stay at Newcastle.
Speaking to Italian media as he departed Milan airport on Thursday morning, Tonali explained his decision to leave Newcastle United.
"We decided to make a change, so we are ready for this new adventure."
He added that the transfer had been amicable on both sides.
"Newcastle wanted the best for me, and I wanted the best deal for Newcastle. So we are all happy, and I am ready for this new challenge."
Asked why he had chosen Tottenham amid reported interest from Arsenal, Manchester City and Manchester United, Tonali pointed to De Zerbi's influence.
"Let's say that Roberto De Zerbi did a great job, had a big impact in all this. It is a life choice for my family, because we come from three years at Newcastle, and our lives change with our child's birth. So we decided to change a bit."
"De Zerbi made a great difference. He did his job, and he did it very well."
Asked whether he would be interested in a return to Serie A in the future, Tonali left the door open.
"It's always been very difficult; there's never been an opportunity, even though we've talked about it. We joke about it all the time, but if the opportunity arises, maybe one day we'll talk about it seriously."
De Zerbi is thought to have been a key influence in convincing Tonali to make the move to north London.
The Tottenham manager has played an important role in helping the club attract top talent this summer, despite successive 17th-place finishes in the Premier League.