The 30-year-old centre-back has joined the struggling Serie A outfit on a six-month loan from Spanish club Sevilla with an option to buy, with Ibrahimovic also recruited by the club this month.
"I've come across him on plenty of occasions throughout my career," Kjaer told a press conference.
"We’ve had a few battles on the pitch but there’s no problem between us now, we’re working towards the same goal."
The former Fenerbahce player had blasted Ibrahimovic as "arrogant" after the Swede grabbed him by the throat during a Europa League group stage match which Manchester United lost 2-1 in November 2016.
"His presence here is an extra push for everyone, he's a great champion and his career speaks for itself," continued the Denmark captain.
"It's a pleasure for everyone to have him in the team."
Kjaer had been on loan at Serie A club Atalanta since last September but had played just six times for the Bergamo side.
He also previously played for Italian clubs Palermo and Roma.
"AC Milan has always been a dream for me, when the chance came around I jumped at it," he added.
Seven-time European champions Milan are 10th in the Serie A table, 10 points off the Champions League places.
Kjaer has captained Denmark since 2016, scoring three goals in 95 appearances.