"The gaffer (Sir Alex Ferguson) spoke to me about going on loan to Swansea and said it would be a good move to gain experience and for my development," Brandy told the club's official website.
"I'm looking forward to the challenge. My target is to get into the first team and show what I can do, score a few goals and help Swansea gain promotion.
"If I can do well for Swansea then perhaps the boss will give me a chance when I go back to United."
Swansea manager Roberto Martinez, who could hand Brandy his debut against Port Vale on Saturday, has been on the youngster's trail for some time.
Martinez said: "He is highly regarded at Old Trafford and we are grateful to Sir Alex for allowing him to join us.
"Febian is a very exciting talent who we have been chasing for quite some time. He has great pace, skill and holds the ball up really well for his size."