The 22-year-old penned a one-month deal at Highbury back in February and has gone on to make seven appearances for the Cod Army.
With Graham Alexander's squad chasing promotion to Sky Bet League One, Morris will now remain a part of that bid.
"Josh has settled in really well since he joined us from Blackburn Rovers last month," Alexander told Fleetwood's official website.
"He is playing very well and he is causing the opposition problems down the left-hand side of midfield. He has shown he is a young player with a bright future ahead of him.
"He shows a lot of quality on the ball and he is a good part of the squad. I am pleased he is staying and we thank Blackburn for allowing us to keep him."