"Yes, he is," Southgate told reporters on Thursday when asked if Rooney will captain the side against Scotland.
The 31-year-old Rooney recently broke his 11-game lean spell for United when he scored in the 2-1 Europa League defeat by Turkish side Fenerbahce last week. He subsequently returned to the club's Premier League starting line-up in Sunday's win over Swansea City.
"(Rooney) is in a better place than he was (before) ... in terms of his sharpness. There was no hesitation from me in selecting him," Southgate added.
"He's playing well for Manchester United, I think he's a player who (needs to) get into a rhythm.
"Wayne uses his experience very well, especially for the younger lads. He's a big part in trying to get the victory."
Following England's goalless draw in Slovenia and an underwhelming home win over Malta in World Cup qualifiers last month, Southgate has two more games to convince the Football Association (FA) that he is the right man for the job.
Southgate, however, said he has given little thought over the possibility of taking up the England job on a permanent basis.
"For me, what happens to me is not important, we have to win this game for the country, and because we want to be top of the group and heading to Russia," he said.
"100 percent, my focus is on the match and I think it would irresponsible and unprofessional for it to be any other way."
England currently top Group F with seven points from three games, while Scotland sit fourth with four points.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Pritha Sarkar)
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