An investigation is to be carried out into the conduct of Met Police chief Sir Ian Blair after the Tube shooting of Brazilian Jean Charles de Menezes.
Mr Menezes was shot dead at Stockwell Tube station
The Met said it "welcomed" an Independent Police Complaints Commission inquiry but stressed the matter was not solely about Sir Ian.
The victim's family says Sir Ian "misled" the public after Mr Menezes was shot dead on 22 July by police.
Early reports suggested Mr Menezes, 27, fled from London anti-terror officers.
He was shot eight times, including seven times in the head, at Stockwell Tube station after officers mistook him for a suicide bomb suspect.
On the day of the shooting Sir Ian told a news conference that, as far as he understood, the shooting was directly linked to the anti-terrorist operation following the failed suicide bomb attacks on London the day before.
Scotland Yard was also quoted as saying Mr Menezes' "clothing and behaviour" added to suspicions he was a suspected suicide bomber.
On Monday Deputy Assistant Commissioner John Yates issued a statement on behalf of the Met.
He said: "The Metropolitan Police welcomes the appointment of an investigating officer to consider these further complaints raised by the family of Jean Charles de Menezes."
He added that "all of those involved" would "co-operate fully" with the investigation.
Regarding inaccuracies widely reported in the aftermath of the shooting, the Met said a private apology had been made to Mr Menezes' family 48 hours after the shooting.
The statement said the police did not correct inaccurate information already in the public domain because the IPCC had "asked all parties involved not to comment once their investigation started".
The Menezes family lodged an official complaint alleging that Sir Ian and other senior officers made false public statements following the shooting.
Home secretary approval is required for an investigation into the commissioner of the Metropolitan Police.
Speaking on Monday, the family welcomed the inquiry.
Mr Menezes' cousin Alez Pereira said: "This is fantastic news and a great victory for our campaign."
And family lawyer Harriet Wistrich told BBC News: "We're pleased that they are now investigating that and that the home secretary has approved an investigator to look into the conduct of everyone concerned including, ultimately, Sir Ian Blair," she told BBC News.
A spokesman for the Jean Charles de Menezes Family Campaign claimed that senior Met officers had given "off the record" statements to journalists immediately after the shooting.
"We believe these off-the-record briefings were attempts to mislead the public and cover up the fact that the police had killed an innocent man," he added.
The Independent Police Complaints Commission probe will be led by senior investigator Mike Grant, and be separate from the IPCC's existing investigation into the circumstances of the shooting.
IPCC chairman Nick Hardwick said: "Neither we nor Jean Charles' family want this complaint to distract us from the main task of finding out how and why Jean Charles died.
"We still expect our investigation into the shooting to be completed by the end of December."
He added: "We have not made any assumptions and for the sake of Jean Charles' family, officers within the MPS and the public at large, will try to establish the truth in an impartial, proportionate and timely way."
Meanwhile, Liberal Democrat home affairs spokesman Mark Oaten said "lessons must be learned" from the Brazilian's "tragic death".
He added that it was critical to "have confidence in the public statements of the police".
And Shami Chakrabarti, director of human rights group Liberty, told BBC News 24: "It's completely right that the media handling and the statements and the comments that were made about the shooting are dealt with just as robustly as the police operation itself."
A second aspect of the Menezes family's complaint - that Scotland Yard delayed informing it of the death - will be incorporated into the main IPCC inquiry expected to conclude by the end of the year.