The Premier League outfit confirmed on Friday that they had reached an agreement over Essien's switch to San Siro, and that the Ghanaian had traveled to Italy for a medical.
And Galliani insisted the club had been planning the deal over an extended period, with compatriot Sulley Muntari proving instrumental in Essien's decision to make the move.
"We had been chasing him for a few months," he said. "We think he can do very well in (Clarence) Seedorf’s new system, sitting in the two in front of the defence and above all he can be included in the Champions League squad.
"Muntari was one of his greatest sponsors.
"Riccardo Montolivo will be out for two Champions League games and Muntari one, so we needed a midfielder.
"I think he is physically reliable, but he has to pass the medical tests at Milanello and then he can sign."
Milan have had a disappointing season and currently sit 11th in Serie A.
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