Beckford, 26, scored 31 goals for the Yorkshire club last season, the last of which came on the final day against Bristol Rovers, which clinched promotion from League One.
That took his tally for Leeds to 85 in 150 appearances after he joined them from non-league Wealdstone in March 2006.
On the move: Jermaine Beckford is expected to join Everton on a free transfer
Mentor: Everton boss Moyes
Beckford's contract at Elland Road was cancelled last week and he nowsteps into the Barclays Premier League after passing a medical at Everton's Finch Farm training complex.
Beckford is looking forward to pitting his wits against some of the world's top players.
He said: 'I am excited by it. It's going to be a test, I know that, but I am looking forward to it. I want to test myself at the highest level and luckily for me, David Moyes showed an interest in me, showed some faith in me and hopefully I can repay that.
'I've been impressed a lot by him. He seems like the type of guy who will sit down and tell you where you're going wrong, what you're doing right and what you might need to work on.
'It is a club I can learn from and it can help me develop into a better player. Fingers crossed, I can be really involved in taking this club where it wants to be.'
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