AEG also is the owner of LA Galaxy, the MLS club where Ibrahimovic had played between March 2018 and the end of the most recent season.
The 38-year-old has a 50% stake in the club and spoke of his excitement at his new role.
"Hammarby is a great club, with passionate supporters and a respected history in Stockholm and throughout Sweden," said Ibrahimovic.
"I am excited for the opportunity to continue my relationship with AEG while supporting one of the most interesting and influential clubs in Sweden."
AEG president Dan Beckerman added: "Hammarby is one of the most historic clubs in Swedish football and we believe that adding Zlatan Ibrahimovic, one of the world's most respected and experienced players, will create additional opportunities for the club.
"AEG will continue to hold our remaining ownership shares in Hammarby and support the club's operations and development, but now it will be in collaboration with one of the most knowledgeable and iconic players of all time."
Hammarby finished third in the Allsvenskan last season, a solitary point behind champions Djurgardens.