The new deal will keep Davies at Nottingham Forest until the summer of 2017.
Nottingham Forest chairman Fawaz Al Hasawi said: “This is a fantastic day for Nottingham Forest.
“Billy and I have the same long-term vision for the club and I am absolutely delighted that he has agreed to sign an extension to his contract.
“I look forward with great excitement to working alongside him for many years to come as we aim to bring success back to this magnificent club.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.