The Electoral Commission has apologised to his family for allowing Britain First to put "Remember Lee Rigby" on voting slips in European elections. The watchdog said the use of his name had caused "deep offence and distress".
The system of checks would be tightened to ensure a "similar mistake is never repeated", the regulator added.
The commission's director of party and election finance, Peter Horne, resigned last week amid a row over the use of Mr Rigby's name by Britain First, which is fielding candidates in Wales in European polls later this month. Britain First applied to use seven slogans in the elections and four were rejected, but the remaining three, including the one relating to Fusilier Rigby, were approved by the watchdog.
Although the slogan cannot be used in future elections it can still feature on ballot papers on 22 May, the first anniversary of Fusilier Rigby's death.
The 25-year-old father was killed near Woolwich Barracks in south-east London.
Electoral Commission chairwoman Jenny Watson said she had spoken to Mr Rigby's family to apologise, saying the commission was "deeply sorry for this mistake and the pain that it has caused".
An independent investigation into the watchdog's decision found that Mr Horne "remembered thinking that it was distasteful but not sufficient to cause offence".
Although the review found the staff involved acted largely within the commission's processes, they failed to consider any need to protect public safety, morals or the rights and reputations of others.
Elizabeth Butler, who carried out the investigation, said the watchdog must introduce checks when personal names are used in party names or descriptions to ensure the individual or their family has consented, and review all names, descriptions and emblems currently on the register.
She has called on the watchdog to consider the wider context when approving party names and descriptions and involve more senior officials in the decision.
The watchdog said it would accept all of her recommendations as soon as possible.
Britain First says it is not a "normal" political party but regards itself as a "patriotic resistance" and "street defence organisation" which backs an end to all future immigration and wants to "restore Christianity as the bedrock and foundation of our national life".
Cabinet Office minister Greg Clark said: "The use of Fusilier Rigby's name in an attempt to make political gains is disgraceful and intolerable, and my heart goes out to his family, friends and colleagues for having been put through this painful and totally unacceptable experience.
"It was an appalling error by the Electoral Commission to approve this clearly offensive description. They have accepted full accountability for this, and the government notes that the director of party and election finance has resigned.
"As soon as the incident came to light, I wrote to the Speaker in his capacity as chairman of the Speaker's Committee, which oversees the Electoral Commission, to ask the committee to ensure there was a full, independent investigation and to ensure that steps were taken so that it could never happen again.
"The government explored every possible avenue to try to prevent the offensive ballot paper being issued, including changing the law, but because the election was already under way it was made clear that this could not legally be done without prejudicing the proper conduct of the election, in particular by disenfranchising overseas voters, including members of the armed forces serving overseas.
"The Speaker's Committee and the Electoral Commission have accepted the report and its recommendations. It is essential now that the commission provides public assurance that this cannot, and will not, ever happen again."
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