The Toffees confirmed on their official website four days ago that the 23-year-old shot-stopper has joined from Sunderland for a club-record fee.
Pickford made the move to Merseyside from the north east after the Black Cats had suffered relegation to the Championship during the previous campaign.
Despite Sunderland finishing bottom of the Premier League table, Pickford’s performances between the sticks stood out, with the youngster’s distribution and reaction saves receiving great praise.
Former Wigan keeper Kirkland spoke highly of Pickford’s ability and claimed that the Red half of Merseyside could have signed him for a lot less.
“He is something special,” Kirkland told Sky Sports. “I told Liverpool to sign him 18 months ago. You could have got him for a lot less then.
“He’s the best I have worked with. He’s a very confident lad and he doesn’t have a weakness in his game.
“Normally with goalkeepers sometimes they are struggling with one aspect of the game but this lad has got the lot.
“His distribution is second to none, he makes the saves which ‘keepers should make and his command of his box is the best I have ever seen.”
At this moment in time, Pickford is away on international duty with the England Under-21s where he is hoping to help his home country win the European Championships.
During the opening match of the campaign, Pickford helped the Three Lions record a goalless draw against holders Sweden, mainly thanks to his second half penalty save.
Upon his return, he will join an Everton team that will be looking to qualify for the group stages of the Europa League after they finished seventh last term.
On the other hand, Liverpool will be hoping to qualify for the group stages of the Champions League after securing fourth spot ahead of Arsenal on the last day of the season.
Jurgen Klopp utilised Simon Mignolet and 2016 summer signing Loris Karius between the sticks during the recently concluded campaign, with the latter receiving criticism for his performances.