He spent the end of last season training with Avenue's first team, combining it alongside his studies with Doncaster’s academy.
Whiting captained Rovers' U18s last season and was also named as an unused substitute during the club's EFL Trophy clash with Newcastle United U21s.
"It’s a deal I’m happy to get over the line," Whiting said.
"The quality of the squad is high and hopefully this season we can get the club back to where it belongs."
Avenue boss Mark Bower said: "Jak impressed us in training at the back end of last season.
"He has some really good attributes and we’re looking forward to working with him to help him reach his full potential."
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