Negotiations accelerated quickly after Lampard's arrival was confirmed on Monday afternoon with a deal between the two clubs understood to see Alli arrive on a free transfer with Everton required to pay £10 million once the 25-year-old plays 20 games.
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Sources confirmed there are further performance-related add-ons which could see the fee reach at least £30m with Alli signing a two-and-a-half-year contract.
Alli started just four matches since Antonio Conte took over as Spurs head coach in November and is desperate to revive his career after dropping out of Gareth Southgate's England squad, having last made an international appearance in June 2019.
Alli joined Spurs from Milton Keynes Dons for £5m in February 2015 and became one of England's stars with a total of 51 goals and 181 Premier League appearances.
Newcastle, Southampton and Valencia were among several clubs to express an interest in Alli and it initially appeared Everton would find a deal difficult to complete given Premier League rules dictate they had to find a permanent agreement.
No top-flight club can loan more than two players from other Premier League sides at once. Everton signed Anwar El Ghazi on loan from Aston Villa under Lampard's predecessor Rafa Benitez and have also signed Manchester United's Donny van de Beek until the end of the season.
Last summer, Spurs chairman Daniel Levy blocked a loan bid for Alli from Paris Saint-Germain -- now managed by former Spurs boss Mauricio Pochettino -- but the club have not stood in his way this time.