The former Cobblers player steps up from under-18 coach while Trevor Gould will head up the centre of excellence.
Chairman David Cardoza told the club's website: "They both know the club, they know the coaches and they know the players currently in the system."
He added: "They have built up a lot of contacts with local clubs, managers and coaches over the last few years.
"Knowing the local football scene and having contacts there is very important."
At the end of April, Parrish had been linked with the manager's job at another of his former clubs, Telford.
He told BBC Radio Shropshire at the time: "It does appeal to me. If I can help out in any way then I might look to do that."