"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."