The PA news agency understands that, after days of negotiations, a deal was struck between the two Premier League clubs on Thursday.
Spurs had quickly set their sights on Frank after Ange Postecoglou was sacked last week - only 16 days after he secured Europa League success - and made an official approach to Brentford on Monday.
Discussions between Tottenham and Brentford initially centred on Frank's current terms at the west London club, which were set to run until the summer of 2027 and contained a release clause reportedly in the region of £10million.
Further talks were required over which backroom staff Frank would take to Spurs but, eventually, a deal has been struck.
Highly-rated Brentford first-team coach Justin Cochrane is set to follow Frank to Tottenham and, in the process, return to the club where he started his coaching journey.
London-born Cochrane has been part of Frank's backroom staff since 2022, after he initially developed as a coach in Spurs' youth-team before a spell at Manchester United.
Cochrane, 43, has earned a reputation as one of the brightest coaches in England and earlier this year joined Thomas Tuchel's coaching staff for the national team alongside his role at Brentford under Frank.
Frank would take over a Spurs side which won a trophy for the first time since 2008 with victory in the Europa League final last month but finished 17th in the Premier League.
The ex-Brondby boss has transformed Brentford during his seven-year spell in charge, with promotion from the Championship in 2021 followed by him establishing the club as a Premier League regular despite a modest budget.
Later on Thursday, Tottenham announced Australian Mile Jedinak, Nick Montgomery and Sergio Raimundo - three members of Postecoglou's backroom staff - had officially left the club.
Ryan Mason departed earlier this month to accept his first managerial role at West Brom.
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