Yakubu failed to meet the government department's criteria for international appearances over the last two years.
But, after an appeal hearing in Sheffield on Wednesday, the Home Office agreed to relent, allowing the deal to go through - and Yakubu has signed a five-year contract.
The 24-year-old becomes Everton's record signing, outstripping the £8.6million David Moyes agreed to pay Crystal Palace last summer for Andrew Johnson, and he could now make his debut at Bolton this weekend.
Yakubu told evertonTV: "I am happy to be here. It is a great feeling to come over and meet a lot of good players and see the spirit that they have.
"I have always said that I want to play for a club that plays in Europe, and I think they have the ambition to move forward and they want to finish in the first four and the Champions League and UEFA Cup and for me that is my dream.
"I know there is a long way to go and I want to be part of that - to be successful and to have that dream."