The Ukraine striker endured two disappointing years at Chelsea following a big-money transfer from Milan but sealed a move back to Serie A when the two clubs agreed a deal on Saturday - although it is still subject to a medical on Monday.
"This is a family and we're all happy," he told Gazzetta dello Sport. "It's not true that only Silvio Berlusconi insisted that Andriy return. I've put my weight behind the cause too and I'm happy that in the end we've succeeded in bringing him home."
Shevchenko's new team-mates have also declared themselves happy with his return.
Ronaldinho, Clarence Seedorf and Kakha Kaladze have all spoken of their delight at the move, while star player Kaka revealed on Monday he was "extra happy that Sheva has returned".
Following a medical on Monday Shevchenko is set to train individually before joining up with the rest of the squad when they return from having played a friendly in Spain.
It is still uncertain which number the former Milan number seven will wear, although the current occupant of Shevchenko's old shirt - Alexandre Pato - has already revealed he is willing to give up the number.
"We'll talk about it," Galliani said. "Maybe our baby (Pato) will give Sheva his number seven back, but it's not fair to ask him."
On the matter, Shevchenko himself added: "That's nice of Pato to say that, but as far as I'm concerned number 76 would do fine too, or 70 or 77. For me it's just enough that the number's on a Milan shirt."