The 22-year-old central defender swapped recently relegated Championship club Norwich City for Everton in an initial £25m deal before the international transfer window shut.
Godfrey put pen to paper on a five-year deal with the Toffees and immediately linked up with Boothroyd’s England Under-21 squad for their games against Andorra and Turkey.
Having worked with the youngster at Under-21 level, Boothroyd is well placed to provide feedback on him and is confident that he will compete with Yerry Mina and Michael Keane for a place in the starting eleven at Everton.
The English tactician also feels Godfrey can handle the pressure at Everton and expects the defender to kick on and get better under the management of Carlo Ancelotti.
“He’ll bring competition [to Everton’s defence] first“, Boothroyd told The Athletic.
“He’s got two guys ahead of him initially and he’s got to make a stake for his place, which he will.
“He’s the sort of guy that can handle the pressure of going into an environment like that.
“He’s got a top manager and coaching team to work with, and they’ll help him become an even better player than he was at Norwich.
“He’s got to kick on because the Premier League is a lot more forgiving than the Championship.
“I’m sure he will.”
Godfrey could be in line to make his debut for the Toffees when Merseyside rivals Liverpool visit in the league on Saturday.