Olmert is already serving a 19-month sentence after being convicted of bribery and obstructing justice.
The court this week unanimously rejected the appeal of a separate set of charges that included accepting cash-stuffed envelopes from a US businessman. He began his sentence in February.
Olmert was a longtime fixture in Israel's hawkish right wing when he began taking a dramatically more conciliatory line toward the Palestinians as deputy prime minister a decade ago.
He played a leading role in Israel's withdrawal from the Gaza Strip in 2005.