A mother who was arrested on suspicion of murder after her son died of natural causes and been paid undisclosed damages by police.
Abby Podmore, from Quinton, Birmingham, was held in police custody overnight in February 2011 by officers investigating the death of three-year-old Alfie.
Chief Inspector Garry Billing, from Birmingham Police's Child Protection Unit, said: "A payment has been made to Abby Podmore; she's accepted it is a full and final settlement and without any admission from West Midlands Police.
"Ms Podmore was arrested following her son's death as it was deemed in the best interest of the investigation at that stage; she's since recognised that police were acting on information available to them at the time and needed to fully investigate matters.
"It became apparent, however, the case should not be treated as a murder inquiry and she was quickly dismissed as a suspect.
"This is a truly tragic case and no amount of money can ever compensate for the death of a child."
Abby has already received a five-figure out-of-court settlement from Birmingham Children's Hospital NHS Foundation Trust after it admitted failings in medical care prior to her son's death.
An inquest held in September 2011 heard the toddler died of a chest infection after being misdiagnosed by hospital staff.
In a statement issued by law firm Irwin Mitchell, which represented Abby, she expressed relief that legal proceedings against the hospital and police had been concluded.
She said: "Alfie was adored by his family and everyone whose lives he touched during his short time with us and he will never be forgotten.
"I'm just relieved the legal battles with both the NHS Trust and police are now over as we can finally look to begin rebuilding our lives."
An inquest held in September 2011 heard that Alfie died of a chest infection after being misdiagnosed by hospital staff.
Tom Riis-Bristow, a medical law expert at Irwin Mitchell's Birmingham office, who led the legal action, said: "The consequences of losing Alfie so suddenly and in such tragic circumstances have had a long-lasting psychological effect on Abby.
"The out-of-court settlements will be used to help fund the ongoing psychiatric care she needs and will also provide the couple with funds to help them move house, as their present home has so many painful memories which they have understandably found extremely hard to deal with.
"Following our investigations, the hospital has assured Abby that the internal investigation carried out after Alfie's death has led to important lessons being learnt and a number of changes to procedures have since been made which will hopefully mean that no other family has to suffer the same heartbreak."
In a statement to Alfie's inquest, Abby described her arrest as a 'horrifying' event which had robbed her of the chance to grieve.
The inquest heard that antibiotics may have saved Alfie, but he was instead given antacid medication and died at his home on February 6, 2011.
West Midlands Police made the out-of-court payment to Abby without admitting any wrongdoing on behalf of the force.