Alex, left out of his country's World Cup squad, arrived in Milan for a medical and is set to sign a two-year contract with the seven-times European champions.
"I'm very happy to be here at Milan, everyone has said good things about the club to me," he told Milan's TV Channel.
"I want to begin working hard to prepare well for next season in which I want to help take Milan back into the Champions League.
"I'm really excited to be able to pull on the Milan shirt and I'm ready to fight for the team and the club."
Former Chelsea defender Alex made 31 league appearances and scored two goals for PSG last season as they won their second successive French league title and reached the Champions League quarter-finals.
Milan are also poised to sign PSG winger Menez on a free transfer. Italian media reported that he will join the Serie A club on a three-year contract.
Former Milan striker Filippo Inzaghi has not been officially announced as the club's new coach but was seen meeting Menez in Ibiza with chief executive Adriano Galliani and is strong favourite to take over the job from Clarence Seedorf.