The officer, Ahmed al-Mreyssi, died after being repeatedly run over during anti-government protests.
The court upheld a life sentence given to a second man in the case.
Bahrain and its Sunni royal family have been shaken by unrest since pro-democracy protests began in 2011. Most protesters are from the Shia majority.
The death sentence was confirmed on Wednesday for Ali al-Taweel, and the sentence to life imprisonment for Ali Shamlo.
Lawyers for the two men have said they will appeal against the decision at the court of cassation in a final effort to have the sentences reduced.
Bahrain's largest opposition political party Al Wefaq denounced Wednesday's decision and said confessions used as evidence in convicting the two men were extracted by torture.
The Gulf island kingdom has been wracked by nearly two years of violence that followed the clearing of an iconic landmark, Pearl Roundabout, in the capital Manama, in February 2011.
As violence escalated 35 people, including five police officers, were killed. Hundreds more were hurt and thousands jailed - the vast majority Shia Muslims.
Since then, opposition and human rights activists say another 45 people have been killed, a figure which the government disputes.
In October last year two policemen died of injuries sustained during clashes with protesters in villages outside Manama.
Last December, a Bahraini court commuted to life imprisonment the death sentences of two other protesters convicted of killing two policemen in another incident in 2011.
A Bahraini appeals court on Wednesday upheld a death sentence against a protester convicted of murdering a policeman in March 2011.