City boss Alex Inglethorpe told BBC Radio Devon: "He's 24 years of age and he fits the bill of the type of player that will help us next season.
"I liken him to Tim Cahill of Everton. He likes to get forward and score goals, and has a good grounding in both League and non-League football."
Terry Brown was not surprised to see interest in Challinor - who was also a target for Woking.
Brown told BBC Southern Counties Radio: "He's a talented boy and people love goalscoring midfielders.
"The decision also frees him up to get regular first team football. I just need to get the balance right."
Challinor scored nine goals for the Shots this season helping us to our fourth place finish.