Campos was a replacement for veteran former world champion Humberto Soto, who was injured.
The 27-year-old Scot extended his winning record to 12 fights, 11 by knockout, and feels he is on the way to the top.
Taylor commented: “I always believed that I could become a world champion, I can smell it now.
“My dream is so close to becoming a reality, I am very satisfied with the beginning of my career.
“I thank Barry McGuigan for the opportunities that he gave me. I’m going to work hard until it becomes reality.”
McGuigan said: “Taylor is ready for a world title challenge. we are aiming for the winner of the March 17 clash between José Ramírez and Amir Imam, who are fighting for the vacant WBC title.
“Josh is one of the best fighters in the world, not just at 140 pounds, but anywhere else.
“We are now very close to being world champions,” he added.