Gary Waddock left for Wycombe Wanderers and Williams will be number two to Jason Dodd, whom he played with at Southampton.
Speaking to Get Hampshire, Dodd said: "Paul is very similar to me. Aldershot are a footballing side and we both like that way of playing. He is someone I can trust and the players will have a good rapport with him.
"He will bring out the best in me and vice versa. That way we have a good chance of putting our stamp on things here.
"As young coaches you need experience but it is very difficult to get that experience. But we have got our foot in here, let's enjoy it and see where it takes us."
Meanwhile, Williams former City team mate Noel Whelan faces a six week lay off after injuring his hamstring on his debut for Darlington against Dagenham & Redbridge last week.
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