Atkinson, a former Aston Villa Sheffield Wednesday and Ipswich Town star, died after Pc Benjamin Monk used excessive force in kicking the 48-year-old in the head at least twice and also used a Taser on him.
The footballer died in hospital after losing consciousness following his arrest near his childhood home in Meadow Close, Telford Shropshire, in August 2016.
The letter, seen by the PA news agency, is from Pippa Mills, the new head of the force, who took over from Anthony Bangham in September.
In the document, she wrote that due to the European Convention on Human Rights, there was an “obligation” for her to write to them on behalf of the force to “acknowledge and accept” that his human rights were breached in this case.
Monk was convicted of manslaughter and jailed for eight years in June.
Jurors heard he fired a Taser three times, including a single 33-second discharge, and left two bootlace prints on Atkinson’s forehead.
Monk was subsequently dismissed from the force the following week.
The letter said: “A police uniform does not grant officers immunity to behave unlawfully or to abuse their powers.
“Ben Monk’s conduct was in direct contradiction to the standards and behaviour of the policing service, and understandably undermined public confidence.”
She added: “I am deeply sorry for the devastating impact the actions of a West Mercia officer has caused you and I extend my deepest condolences to you all, and Dalian’s wider family and friends.”
Ms Mills also said she recognised the incident was “devastating” for the family, adding: “I cannot imagine the immense pain you have felt and how the significant delays with the trial have also added to your burden of grief.
“You have demonstrated great strength and dignity throughout the past five years.”
The family’s lawyer, Kate Maynard of Hickman and Rose solicitors, said in a statement the official apology is “welcomed and overdue”.
“The chief constable’s acknowledgement that a police uniform does not grant immunity is especially pertinent in a year that has seen other terrible examples of deadly police violence,” she told PA.
“With the first conviction of a serving police officer on a manslaughter charge connected with his policing duties in over 30 years, it is hoped that this will serve as a deterrent, and also embolden those who seek police accountability.”
West Mercia Police has been contacted for comment.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in