McLeish raised eyebrows when he left arch-rivals Birmingham City to take over the vacant managerial reigns at Villa Park in June.
Moyes, though, insists his fellow Glaswegian will not be fazed by the challenge ahead, stating: "I am not surprised, but it was a difficult move.
"If anybody knew Big Alex as a player they would have told you it was tough but he wouldn't hide away from any challenge or battle.
"It doesn't surprise me. It's a good move for him, the right move at the time."