The former Republic of Ireland international has worked with Arsenal’s academy for the last 17 years, but often combined his stint with roles elsewhere including spending a number of years assisting Giovanni Trapattoni with Ireland..
Arsenal has said they are discussing potential other roles for Brady at the club.
Gunners chief executive Ivan Gazidis said: "Liam has a deep understanding of what it takes to discover and develop a talented youngster into someone who can perform at the highest level. He has made a massive contribution to Arsenal Football Club.
"It will be difficult to find a worthy successor but we will be looking for someone who can build on what Liam and his team have created."
Brady (56) started his career with Arsenal as a schoolboy in 1971 and made his professional debut in 1973.
He managed Celtic and Brighton and Hove Albion before taking over Arsenal's academy where he developed current first-team players like Jack Wilshere and Kieran Gibbs as well as England defender Ashley Cole who has since moved to Chelsea.