"We have signed an agreement which defines the investment and management rights in accordance to the club's statute and legislation that is in force in Bosnia," Sarajevo general director Dino Selimovic told Reuters.
Selimovic declined to provide details on investment but local media reported on Wednesday that the Malaysian billionaire has pledged to invest 3 million Bosnian marka £1.28m).
Sarajevo, established in 1946, has faced bankruptcy over millions of marka in accumulated debt.
Tan, who has been in talks with the club's managers since last summer, wanted them to draft a plan of the debt restructuring and a three-year investment plan, Sarajevo vice president Edis Kusturica told the Nezavisne Novine daily.
Under the deal, Cardiff will cooperate with Sarajevo, exchanging players and taking part in a football academy, yet to be established, which Tan has said would lure new talents.
"We plan to play friendly games, exchange players, organise joint training camps and marketing campaigns," Tan told the Sarajevo daily Dnevni Avaz in an interview in September.
"I am very optimistic and hope that this cooperation will be very useful for both clubs and for Bosnian football generally," he added.
Local media reported that Tan would not change the Bosnian club's badge and colours, as he did at Cardiff, angering fans.