The boyhood Rossoneri fan is expected to sign a four-and-a-half-year deal with Milan, and Galliani is delighted with the transfer.
"I certainly do not have to introduce Mario Balotelli," Galliani told the club's official website.
"It is a dream come true and something that we all wanted, with the president Silvio Berlusconi at the forefront.
"With the arrival of Mario, we have strengthened our team a lot. We have worked so hard and Mario has been in our hearts for a long time and finally we have succeeded in signing him."
Balotelli joined the Premier League champions from Inter Milan in 2010.