The Toffees confirmed earlier this month that Davies was one of three players to be offered a new deal alongside Seamus Coleman and Andy Lonergan.
Davies has taken time to consider his future, but he has now decided to end his 13-year association with the Merseyside club.
The midfielder, who joined the club at the age of 11, rose through the academy ranks before making his senior debut in April 2016.
Davies went on to make 179 competitive appearances for the Toffees, scoring seven goals and providing eight assists.
However, he has struggled for playing time in recent times, starting just six Premier League games across the last two seasons.
Everton Director of Football, Kevin Thelwell told the club's official website: "We offered Tom a new contract, but he feels he has reached the stage in his career where he needs regular first-team football and, as a result, he wants to look at alternative options away from Everton.
"As a lifelong Evertonian and proud Scouser, Tom has always given everything for the club. We respect his decision and thank him for his service and commitment. Everyone at Everton wishes him the very best for the future."
Davies has skippered England at every age group from the Under-15s to the Under-21s, and he also became the youngest captain in Everton's history at 20 years and 60 days, wearing the armband in an EFL Cup tie against Rotherham United in August 2018.
Everton have already confirmed that Yerry Mina, Andros Townsend and Asmir Begovic will depart when their contracts expire at the end of this month.