The 20-year-old had loan spells with Notts County and Burton Albion last season, but failed to score for either club in six appearances.
Blyth joined Leicester in May 2012 after scoring 17 times for Leamington in the Southern Premier League.
"He's got a terrific record in non-league for scoring goals. He's a big, strong and mobile guy," Northampton manager Aidy Boothroyd told BBC Radio Northampton.
"Whether Clive Platt is struggling [with injury] or not, if Jacob does as well as I expect him to, I'll be pushing to keep him.
"I had Ben Foster [at Watford] who hadn't been a goalkeeper until he was 15. Sometimes, either they haven't played or get picked up late."
Blyth could make his Northampton debut against Newport County on Saturday.