The Welsh international completed a £45m move to Spurs from Nottingham Forest late on deadline day as the club look to replace Harry Kane.
Johnson scored eight goals and registered three assists in 33 Premier League starts during an impressive first season in the top flight for a Forest team who successfully battled relegation.
The 22-year-old is in line to make his debut on Saturday when Ange Postecoglou’s side look to continue their encouraging start to the season at home to Sheffield United.
Former Tottenham star Bale, who also played alongside Johnson for Wales, has echoed those comments.
“He’s doing well, he’s doing well,” said Bale when asked about his compatriot.
“I think the more he plays now in the top flight, the better he’ll get. Like you said, the sky is the limit.
“I think as long as he’s playing football and improving, it’s good for Tottenham and it’s good for Wales also.”