The Islamic court convicted the defendants of "spreading corruption on earth", a capital offence, and ordered them to repay funds embezzled from, among others, state-run National Iranian Oil Company (NIOC), judiciary spokesman Gholamhossein Mohseni Ejei said on live television.
The defendants can appeal against the ruling.
"The court of first instance ... sentenced the three defendants to death," Ejei said in a weekly news conference.
The three were also ordered to pay a fine equivalent to one fourth of the sums they had laundered, he said.
By his own account, Zanjani for years arranged billions of dollars of oil deals through a network of companies stretching from Turkey to Malaysia and the United Arab Emirates. Zanjani amassed a fortune of $10 billion - along with debts of a similar scale, the tycoon once told an Iranian magazine.
At the time of his arrest in Dec. 2013, a judicial spokesman said "he received funds from certain bodies ... and received oil and other shipments and now has not returned the funds".
Prosecutors accused him of owing the government more than $2.7 billion for oil sold on behalf of the oil ministry.
Iran emerged from years of economic isolation in January when world powers led by the United States and the European Union lifted crippling sanctions against Tehran in return for curbs on Tehran's nuclear ambitions.
