The High Court said that London's Metropolitan Police is to go on trial next October on health and safety charges over the charges.
Michael Mansfield, the lawyer representing the family, argued before three of the country's senior judges that failure to prosecute amounted to a breach of article 2 of the European Convention on Human Rights - the right to life.
Lawyers for the group won permission for a judicial review into The Crown Prosecution Service (CP) decision at the High Court, arguing that there was enough evidence to take action against specific officers, including prosecuting them on murder charges.
The Metropolitan Police has denied the charges brought against it as an organisation, saying its officers had not committed criminal acts and has given them its full backing.
The court hearing is expected to last two days.
De Menezes was shot eight times, seven times in the head and once in the shoulder, in the carriage of a Northern line train on the morning of July 22, 2005, at the height of a massive security alert in London.
The incident happened the day after detectives said four men had tried to set off bombs on three underground trains and a bus in a bid to copy the suicide bombings on July 7 when four people killed 52 commuters.
The firearms officers involved have since returned to active duty while Cressida Dick, who was in charge of the operation that led to de Menezes being shot, was selected for promotion in September.