Murphy, who turns 18 on 25th June, will join up with Elliott Dickman's Under-23s side in July.
Born in Annaghdown in the west of Ireland, Murphy joined Galway United's Academy aged 14 and progressed through the ranks before making his first team debut in 2021 aged just 16.
Murphy has captained the Republic of Ireland's under-18 side and was called up for his country's under-19s for UEFA U19 European Championship Elite Phase qualifiers in March.
Steve Harper, Newcastle United's Academy manager, said: "We are very pleased to have secured a deal to bring Alex to Newcastle United.
"He is a very promising young player who has attracted a lot of attention from clubs. It is a real coup for our Academy and is testament to the direction the club is going in under our owners.
"I would like to thank everyone involved with Galway United for their assistance. The club has been a pleasure to deal with and I wish John Caulfield and his players the very best of luck for the rest of the season."
Photograph courtesy of Galway United