The music was written by 17-year-old Mozart in Vienna in1773 as part of his father's attempt to gain a position for young Wolfgang at the imperial court.
The lower part of the manuscript has been in the British Library since 1953, and the other half was purchased from a private owner.
The library will put the work together to mark 250 years since Mozart's birth.
Chris Banks, head of music collections at the British Library, said the manuscript "sheds important light" on the composer's development.
"Mozart was trying to make his mark as a serious composer. He was well known as a child prodigy, but by 17 he couldn't really continue with that."
She said it was a "rare pleasure" to reunite the two halves of the work.
Collecting fashion
It is believed Mozart's widow Constanze, who outlivedher husband by more than 50 years, separated the manuscript in 1835 to boost its value.
His work was increasingly in demand with the dawn of a new fashion for collecting fragments of music manuscripts by the great composers.
The upper portion fell into the hands of a court musician, Julius Leidke.
Constanze sent the lower portion, later acquired by the British Library, to a local government official in Bavaria.
The manuscript contains two new cadenzas to existing piano concertos and a short minuet for string quartet.
The reunited manuscript will go on display in the John Ritblat Gallery at the British Library from Saturday.
news.bbc.co.uk/1/hi/entertainment/4602808.stm
