The inquiry will look at a number of detention operations and how allegations of wrongdoing were investigated by military police, in particular whether there were any cover-ups.
Launching the inquiry, senior judge Charles Haddon-Cave called for anyone with information to come forward.
The families of eight people, including three young boys, who were allegedly murdered by UK special forces in two separate incidents during night raids in 2011 and 2012 welcomed the inquiry when it was announced last December.
"We live in hope that those responsible will one day be held to account," a member of the Noorzai family, one of the families involved, said at the time.
"Over 10 years ago I lost two of my brothers, my young brother-in-law and a childhood friend, all boys with a life ahead of them.
"I was handcuffed, beaten and interrogated outside our family home by British soldiers.
"My relatives and friend were each shot in the head as they sat drinking tea," the family member said.
A member of the Saifullah family added that they were "extremely happy that there are people who value the loss of life of my family, of Afghans, enough to investigate".
Speaking after the inquiry was officially launched on Wednesday, Tessa Gregory, partner at law firm Leigh Day, said her clients looked forward to helping the inquiry team "as they seek to establish the truth which has been hidden for too long".
"Throughout years of secrecy and cover-ups, our clients have fought tirelessly for justice for their loved ones' deaths and they hope that a bright light will now be shone on the practices and command of UK special forces in Afghanistan."
Haddon-Cave said it was "important that anyone who has broken the law is referred to the relevant authorities for investigation".
"Equally, those who have done nothing wrong should rightly have the cloud of suspicion lifted from them.
"This is critical, both for the reputation of the armed forces and the country."
The independent statutory inquiry was commissioned by Defence Secretary Ben Wallace under the 2005 Inquiries Act.
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