Rooney, who will be kept on as captain under Southgate, backed the Under-21 manager's credentials and believes that his four games in charge will be a chance to prove himself at senior level.
"When I first got into the squad [Southgate] was in the squad then. He's done a very job with the Under-21s, and he's got an opportunity to show what he can do at senior level," he told reporters.
"He'll bring his own way of working, it's going to be good to see what that is in the next week. We have to buy into his ways and take his ideas on board. There was a lot of talk over whether I'd be captain or not, so it was good Gareth put that to bed quite early and there wasn't the speculation.
"We've got two games this week that we have to win. Whether that was with Gareth or Sam we have to try and get six points. If we do that Gareth will be happy and we'll be happy."
England scraped a 1-0 victory over Slovakia in their first World Cup qualifier, but sit behind Scotland in the table due to goal difference.