Previously, Beck vehemently denied taking any part in the $6,000 transaction, but documents obtained by The Times showed the chief signed off on the deal.
The department purchased George, a 10-year-old quarter horse, for its equestrian unit earlier this year from Beck's daughter, Officer Brandi Pearson.
Police commissioners said they approved the deal without knowing the horse was owned by Pearson.
Beck said that after reviewing the same documents The Times obtained, he "realized" he had signed the forms approving the deal.
"After evaluating the circumstances of this donation, in retrospect, I should have ensured that the department had formally transmitted to the [Intradepartmental Correspondence to the Board of Police Commissioners] the additional documentation on file which identified the original owner of the horse," Beck said in a statement issued late Wednesday.
"I will continue to work with the commission to increase the department's transparency."
The Times previously reported that in the paperwork sent to the commission by Beck, he assured that "all possible conflicts of interest have been researched and there does not appear to be any issues that would reflect negatively on the department."
In a joint statement with Beck, commission President Steve Soboroff said he did not believe the chief intentionally misled officials so his daughter could profit.
"After reviewing the information provided to date by the department, the inspector general and Chief Beck, I am comfortable that the chief was not involved in the selection, evaluation or purchase of the horse," Soboroff said in a statement.
He added: "Based on the chief's statements today, I am now satisfied the commission will have sufficient disclosure going forward."
Staff writer Joel Rubin contributed to this report.