The promising youngster will continue his career at the Eindhoven side and will ink a contract until June 2018 with his new club
The 19-year-old will sign a five-year deal with the Eredivisie giants upon the completion of his medical on Monday, with the fee believed to be in the region of €8 million (£6.8m).
The Eindhoven side were in the market for a new attacking midfielder due to the expected departure of Ola Toivonen this summer and identified Maher as the ideal candidate to replace him.
"It had been our wish to lure him to PSV for quite some time. I am very pleased with his arrival, because we really wanted him," sporting director Marcel Brands commented on the transfer.
"We have signed yet another talented Dutchman, which suits our philosophy."
Maher came through the ranks of the AZ youth academy and has developed into a key player at the Alkmaar side in the past two seasons.
He had also caught the attention of clubs such as Manchester City, Arsenal, Chelsea and Ajax, but will continue his career at PSV instead.
Maher becomes PSV's third signing of the summer transfer window after the previous arrival of Jeffrey Bruma and Florian Jozefzoon.