The Newcastle United winger travelled to the League Two club last night.
And Roberts – who scored in the club's FA Cup win over Blackburn Rovers earlier this month – completed his move this afternoon.
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The 21-year-old was an unused substitute for Tuesday night's 2-1 win over Premier League champions Manchester City at St James's Park.
North Shields-born Roberts is out of contract at the end of the season.
Speaking after scoring against Blackburn, Roberts said: "Obviously, the aim is to play in the first team. If that's not possible, I'll think about loan options."
Roberts has previously had loan spells at Kilmarnock and Gateshead.