The 500,000 fine plus 250,000 costs come after the firm had already agreed to pay 30 million to Tanzania after entering into a plea bargain with the UK's Serious Fraud Office (SFO).
The ruling ends a six-year inquiry into BAE's activities after it emerged that the arms maker had made payments of around 8m to companies controlled by local adviser Shailesh Vithlani during negotiations to supply Tanzania's Dar-es-Salaam airport with a military radar system.
Justice David Bean, the judge presiding over the sentencing at London's Southwark Crown Court, suggested "there was a high probability" that some of the payments were used to BAE's advantage in negotiations, but it was impossible to determine whether they were lawful.
"The victims of this way of obtaining business, if I have correctly analysed it, are not the people of the UK, but the people of Tanzania," said Bean in his sentencing notes.
"The airport at Dar-es-Salaam could no doubt have had a new radar system for a good deal less than $40m if $12m had not been paid to Vithlani."
While the low fine will no doubt attract criticism from anti-bribery campaigners, it was the result of an American-style plea bargain and is one of the most high-profile deals struck to date by the SFO.
Under the terms of the settlement, the SFO waived its right to investigate any other activities undertaken by BAE before this year if the defence heavyweight pleaded guilty to a single offence.
It was also agreed that any fine handed down by the judge would be deducted from the sum payable to Tanzania, thereby making it in the interests of the court to dish out a lower penalty.
But the plea bargain was yesterday attacked by Bean for being "loosely and perhaps hastily drafted".
He highlighted paragraph eight in particular, whereby the SFO agreed on "no further investigation or prosecutions of any member of the BAE Systems Group for any conduct preceding 5 February 2010".
BAE said in a statement that the ruling, which was delayed by a day, drew a line under "this historical matter".The firm added: "In the decade since the conduct referred to in this settlement occurred, the company has systematically enhanced its compliance policies and processes with a view to ensuring that it is as widely recognised for responsible conduct as it is for high quality services and advanced technologies."
Kaye Stearman, of Campaign Against the Arms Trade, said the original trial judgment was "an indictment of BAE's culpability".
"Whatever the level of the fine, the judge's remarks are damning," she said.
Nicholas Hildyard, of campaigners The Corner House, called for the SFO's practice of plea agreements to be reviewed urgently.