"His attitude last season was excellent and we enjoyed watching a player with Premiership potential.
"He always made it clear that he wanted to come back and join our Championship campaign and we are looking forward to seeing him perform at the next level.
"He's a great addition to the squad."
Manchester-born and raised, Brandy was first spotted playing for his local team, West End Boys, at the age of nine.
He was a regular member of the reserves throughout the 2006-07 season and was the toast of the club in August 2007 when he scored the solitary goal against Juventus to lift the Champions Youth Cup at the National Stadium in Malaysia.
Brandy made his Swans debut as a substitute in the 2-0 win over Port Vale on 19 January and scored three goals in 21 appearances.
He was due to meet up with the squad again on Tuesday, in time to fly out for the club's seven-day tour of Spain.
Meanwhile, Dutch trialist Michael van der Heijden has returned to Holland following a one-week spell that saw him score one of the goals in a 5-0 friendly win over Neath last week.
"We will assess the situation with Michael after we return from Spain,'' said Martinez.
The Swans boss also confirmed that youngsters Kerry Morgan, Kyle Graves and Dion Chambers will join Welsh Premier side Neath next season on loan.
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