The Wolves defender will spend the next three months with the Robins and is looking forward to improving his two-appearance showing so far this season.
"I think it is a good move for me as I want to be playing football," Elokobi told skysports.com.
"There was interest from other clubs, but I decided to come to Bristol City as they are a good club and I can't wait to get started.
"I am not one who is content to sit on the bench. I want to be playing football all the time and hopefully I can do that at Bristol City and add something to the team."