Strachan, 55, was named the new coach earlier this year following a distinguished playing career that saw him earn 50 caps for the Tartan Army.
Discussing the manager's credentials, Norwich City winger Snodgrass has admitted that he can only improve as a player under his guidance.
"I think Gordon can make me a better player," he said. "He made his name as a winger for Aberdeen, Manchester United, Leeds and Scotland, so I'm sure he'll feel he can improve my game. You learn different bits from every manager and that can take you a long way in your career. I'm looking forward to it.
"I'll need to push myself hard to make sure I am part of his plans, and if I get the chance under him I'll need to take it.
"He's got loads of experience at a high level and I think he was the only man for the job. It's up to us now, as players, to ensure he has a successful time as manager."
Strachan's first game in charge will be tonight's clash against Estonia in Aberdeen.