It was announced on Thursday that Moyes would take over as the new United boss once Ferguson retires at the end of the season.
Cahill, who was one of Moyes's most successful signings at the club, says that his former chief fits the bill at Old Trafford.
"You look at any other manager in the world I think, other than Pep Guardiola, there's only David Moyes that would suit a club like Manchester United," Cahill told Sky Sports News.
"He's done so much for the game, and to have the opportunity to go to one of the biggest clubs in the world and continue their level of success is a remarkable measure of the man he is and how much they respect him as a football manager."
Moyes has signed a six-year deal at United.