Symons was appointed assistant boss of the Us eight months ago and has had spells as the caretaker manager of Crystal Palace on two occasions in the past.
The 37-year-old told the club's official website: "Being a manager is something that I've always wanted to do.
"I had a spell at Palace when I was in charg, and I really enjoyed it. It certainly wasn't on my agenda when I came here as Geraint's assistant, because he was someone I knew, liked and respected and I've enjoyed working alongside him.
"[But] the results have been very disappointing and we've all been frustrated by them, but this is an opportunity for myself and one I aim to take."