The 28-year-old, who watched Sunday's 4-0 win over Lecce in Milan's Serie A opener, left their training ground after the tests to join the Sweden squad for their upcoming Euro 2012 qualifiers.
His move, which Milan hope will catapult them back above his former club and perennial champions Inter Milan, is initially a season-loan with the Rossoneri then paying 24 million euros to secure his services permanently.
Milan said in a second statement that on Monday alone 1,137 fans bought Serie A season tickets out of a total of 21,945 sold so far in the two-month sale period.
Ibrahimovic's arrival back in Italy after just a season at Barca has left Milan striker Marco Borriello considering his future given his first-team place is likely to go to the Swede.
Media reports have said Juventus are trying to loan Borriello before the transfer window closes on Tuesday.
"We are talking, soon we'll know more," Borriello told www.gazzetta.it.
Milan, who also boast Ronaldinho and Alexandre Pato in their attacking trident, have also been linked in the media with a late swoop for Manchester City's Robinho while the Rossoneri have said Klaas-Jan Huntelaar could leave, possibly to Schalke.
