The 22-year-old Wales forward becomes the third-most expensive signing in Spurs history, only behind Richarlison and Tanguy Ndombele.
Johnson has signed a six-year deal until 2029 and will take the no.22 shirt.
The deal for the highly-rated Forest-produced talent sees Ange Postecoglou end his first Tottenham transfer window on a high.
The north London side underwent a tumultuous summer, losing all-time top scorer Harry Kane to Bayern Munich for £85m.
Long-time captain Hugo Lloris has also been phased out, but new arrivals James Maddison and Micky van de Ven have so far impressed.
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Johnson's arrival takes Spurs summer spending over the £200m mark, but half of that is offset by Kane's record departure, which could reach £100m with add-ons.
Since his promotion to the Premier League with Forest last year, Johnson has a record of eight goals and three assists in 41 games, while his Wales record reads two goals in 20 caps.
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