The Rossoneri coach revealed his delight at adding the 25-year-old defender to the club's ranks and hopes that there will be further activity before the transfer window shuts
The 44-year-old coach was delighted that the Rossoneri had completed the objective of bringing the Colombian defender to the club and hopes for more signings.
"I welcome the arrival of Zapata. Cristian is one of those players who were on the list of potential acquisitions," Allegri said to Milan Channel.
"He is a player that I had already met in 2006 when I was called by Udinese. Zapata will be able to play in the centre of defence or in the flanks. With him, we are set in defence.
"We'll see for the rest of the departments. There is still 20 days left before the market closes."
Press speculation has also mooted a return to Milan for Real Madrid attacking midfielder Kaka, though, when prompted, Allegri revealed there was nothing to say.
"On Kaka, I can say that currently there is no big news."