Middlesbrough will pay an initial £7m fee, with a further £13m available in add-ons, while Spurs have retained a 20% sell-on clause and matching rights on any future sale.
Blackburn Rovers, who sold Phillips to Tottenham for £2.5m in 2023, are due 15% of the profit from the deal under a sell-on agreement from his original transfer.
The 21-year-old has made more than 100 Championship appearances across his time at Blackburn and subsequent loan spells at Plymouth Argyle and Stoke City, and is expected to play a significant role as Middlesbrough push for promotion back to the Premier League this season.
An England youth international, Phillips came through Blackburn's academy and was regarded as one of the Championship's most promising young centre-backs before his move to Tottenham, though he found senior opportunities hard to come by at the Premier League club and instead built experience through a series of loan spells back in the second tier.
The move is the second time this summer Middlesbrough have signed a player from Tottenham, following the arrival of striker Will Lankshear in a deal that could also be worth up to £20m with add-ons, underlining head coach Kim Hellberg's efforts to strengthen his squad ahead of another promotion push.
For Spurs, it represents a seventh permanent sale of the summer, part of a broader squad clear-out that has also seen centre-back Radu Drăgușin join Fiorentina on loan with a £21.4m obligation to buy contingent on appearance targets.
Tottenham are also expected to complete the permanent departure of versatile defender Djed Spence to Inter Milan in the coming days, continuing a summer in which the north London club have prioritised trimming their squad alongside their own incoming business.