The Rossoneri have completed the transfer of the young defender, while selling half of Alberto Paloschi's rights to Chievo and letting Ferdinando Coppola join Torino
The Rossoneri were in the market for defensive reinforcements following the departure of Francesco Acerbi earlier this winter, and they see Salamon as a valuable long-term addition to their squad.
Salamon, 21, joined Brescia from Lech Poznan at the age of 16, and had developed into an important first-team member at the Serie B outfit after a loan spell at Foggia in 2010-11.
The youngster had also caught the attention of a number of other Serie A sides, but has decided to continue his career at Milan and said he was ready for the challenge of playing at San Siro.
"I am very happy to sign for Milan," he told Sky Sport Italia. "I am not afraid of anything."
Meanwhile, the Rossoneri have opted to sell 50 per cent of Alberto Paloschi's economical rights to Chievo. The attacker is currently on loan at the Verona outfit, and has netted seven goals in 10 Serie A appearances so far.
Additionally, the San Siro outfit have sold goalkeeper Ferdinando Coppola to Torino. The 34-year-old already spent last season on loan at the Granata, and will now return to Turin.