Dowell, 22, had been with the Blues since joining the club’s academy aged seven, but only went on to make five first team appearances.
He was handed his debut by Roberto Martinez in a Europa League dead-rubber at home to FK Krasnodar in December 2014, before making his Premier League bow as a late substitute against Bournemouth at Goodison Park in April 2016.
His first start for Everton in the top-flight came two weeks later, coincidentally against Norwich, when he produced a man-of-the-match performance in a 3-0 final-day home win under caretaker manager David Unsworth.
But Dowell would only enjoy two more first team outings in royal blue; both in the EFL Cup in 2018 against Rotherham United and Southampton.
Since the start of the 2017-18, Dowell has been loaned to Championship clubs on four occasions, making 78 appearances and scoring 17 goals across spells with Nottingham Forest, Sheffield United, Derby County and Wigan Athletic.
He netted two hat-tricks during these loans - both against Hull City - first for Forest in 2017 and most recently for Wigan in their 8-0 thrashing of the Tigers earlier this month.
Dowell was also a regular in Unsworth’s Premier League 2 title-winning Everton Under-23s team in 2017 and in the England side that won the FIFA Under-20 World Cup that same year.
He joins a Norwich side aiming for an immediate return to the Premier League following relegation to the Championship after just one season back in the top-flight.