The Court of Cassation announced its verdict in the presence of 12 of the accused, the source said, adding that the remaining two had been tried in absentia.
A court convicted the defendants of beating the victim to death "for terrorist purposes", the source said, citing the charge sheet.
A semi-military court established under a state of emergency in 2011 had originally sentenced the men to life in prison.
Lawyers for the defendants said their clients were "tortured" while in custody in 2011, and no action has been taken in response to their complaints.
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Scores of Shiites have been jailed over accusations of involvement in violence since protests against the ruling Sunni Al-Khalifa dynasty erupted in February 2011.
Despite a heavy-handed crackdown by security forces in mid-March 2011, supported by Saudi-led Gulf troops, protesters quickly returned to the streets, mainly in Shiite villages, where they frequently clash with police.
At least 80 people have been killed in Bahrain since February 2011, according to the International Federation for Human Rights.