Alli has joined the Toffees on a two-and-a-half-year contract after growing disillusioned with life in North London.
Alli joined Spurs from MK Dons in the summer of 2015 and impressed particularly in his first two seasons at the club, reaching double figures for goals in both campaigns.
His form dropped off in the last two seasons and he struggled for game time under Jose Mourinho and recently Antonio Conte.
The 25-year-old has also lost his place in the England national team but Woodgate believes a change of surroundings can help Alli regain his best form.
"I think he needed to get out of Spurs, to be honest with you," Woodgate exclusively told Stats Perform. "I think in the Pochettino era, he was one of the best players in the Premier League. He was in the England squad regularly and sometimes it's just that manager that really believes in you and gives you that confidence to play well.
"I mean, you don't turn into a bad player overnight. Dele Alli will be good again at Everton, no doubt about that, and with the right manager it'll give him more confidence and put him on a platform to put him in the right position for him to go and do what we know he can do.
"Because at Tottenham, he was scoring goals for fun, he was running forward, he was assisting, he moved a bit like a Rolls Royce-type player. He always had time on the ball, but something hasn't gone right from the last few managers. [Jose] Mourinho, [Antonio] Conte and [Nuno Espirito] Santo. In the Pochettino era, he was absolutely outstanding."
