The court said the three are guilty of "particularly callous and inhumane murders," The Daily Telegraph reported. They included Jeffrey Bamber, 51, who was given a life sentence in 1981 for killing his adoptive parents, his sister and her two young sons.
The three appellants argued that whole-life sentences with little chance of release are inhumane.
Under current British law, judges impose life sentences for murder with a minimum term to be served in prison. With whole-life sentences, only the Justice Secretary can order an inmate's release.
Abu Hamza, a radical Islamic cleric now held in Britain, has filed a challenge with the European court against his extradition to the United States. His lawyers argue he should not be extradited because he faces life without parole in a U.S. prison.
The other challengers in the case decided Tuesday were Douglas Vinter, who was sentenced to life for killing his wife after he was released from a nine-year sentence for killing a work colleague, and Peter Moore, who killed four gay men.