The court also upheld life sentences for six other defendants convicted over what was the deadliest attack on security forces since a Shiite-led uprising was crushed in 2011.
A seventh defendant previously sentenced to life in jail did not appeal because he remains at large, the judicial source said.
A policeman from the United Arab Emirates was among the three officers killed in the Shiite village of Diah in March 2014.
Bahrain, which lies across the Gulf from Shiite Iran and is home to the US Navy's Fifth Fleet, has been rocked by unrest since it quelled Shiite-led protests demanding political reforms in 2011.
Yesterday, a Bahraini court more than doubled the jail sentence against opposition leader Sheikh Ali Salman, in a ruling his bloc warned risked stoking fresh unrest.
The appeals court increased the sentence of the Shiite cleric on charges of inciting violence to nine years from the original four.