"The player has signed a four-year contract," Milan said in a statement without giving details on the permanent transfer.
Milan's capture of Robinho and Zlatan Ibrahimovic from Barcelona last week prompted Marco Borriello, who started upfront in Sunday's 4-0 win over Lecce, to quit for AS Roma in a deal which was only just concluded before the deadline.
"AC Milan announce that Marco Borriello has joined AS Roma on loan," a second statement said.
Dutch striker Klaas-Jan Huntelaar earlier made further room at the San Siro by leaving for Schalke 04.
Milan had been quiet at the start of the transfer window but some limp pre-season displays persuaded owner Silvio Berlusconi to drop his frugal spending policy and bring in former Inter Milan forward Ibrahimovic on an initial loan and sign Robinho.
The 26-year-old Robinho joined City from Real Madrid in 2008 in a big-money deal but never really settled in the Premier League and spent the second half of last season on loan at former club Santos.
"I want to make history with this club. I will give so much happiness to my fans," Robinho told Milan's official website (ww.acmilan.com).
The tricky player will struggle to hold down a first team place with new Milan coach Massimiliano Allegri saying he expects to play a forward trident of Ibrahimovic with Brazilians Ronaldinho and Alexandre Pato.
Robinho has been bought as a deputy for Ronaldinho and Pato but Borriello and Huntelaar's exits mean only 37-year-old Filippo Inzaghi remains as a spare targetman in case of injury or suspension to Ibrahimovic.
Milan have not won Serie A since 2004 and have watched Inter win the last five titles and last term's Champions League.
However, Italian pundits believe their late double-dip into the transfer market makes them clear favorites to be Inter's major rivals this term having finished a lacklustre third behind AS Roma last season.
Cash-strapped Roma swooped for striker Borriello given other new recruit Adriano is out injured.
