Josh Murphy has already made 29 appearances for Norwich, while his twin brother Jacob has made two appearances.
The new deals will keep the duo at Norwich until 2017.
Josh Murphy told the club’s official website: “I’m delighted and I’m just glad it’s all sorted now.
“The club has got a big place in my heart and I’m happy to sign, and now the real work begins.”
Jacob Murphy has immediately joined Coventry on a season-long loan deal.
Coventry manager Tony Mowbray said of his new signing: “I’m delighted to finally get this deal over the line as we’ve been tracking Jacob for some time and beat a number of clubs to his signature.
“I’ve continually stressed the importance of pace from both the wide and central positions, and Jacob is a player who has that attribute in abundance.
“He showed his ability last season by helping keep Colchester United in the league and we’re hoping he can continue to progress this season with us.
“We’re also delighted to get him for the entire season as it gives us a consistent option going forward and it’s another crucial piece of the squad in place.”
— Norwich City FC (@NorwichCityFC) August 14, 2015