The Trotters forward complained that he had been racially abused after the Championship match at The Den on 6 October.
And Millwall have released a statement which read: "Having completed our investigations into the incident, we have identified and interviewed a 13-year-old boy who admitted a verbal exchange with Marvin Sordell in which abuse was used.
"The individual has been banned from Millwall matches for the foreseeable future but, as a club, we also felt, given the boy's age and background, we had a duty to play our part in attempting to educate and rehabilitate him.
"Accordingly, we have offered to put him through one of our education programmes, run by Millwall for All, in the hope that we can change his outlook on equality, racism and life in general.
"In the meantime, the boy has written a letter to Marvin Sordell offering his apology, which has been accepted."
The Millwall statement also made it plain that the club was unhappy with the media coverage of the incident.
The statement continued: "We would also like to put on record how disappointed everybody at Millwall FC was in the way in which the initial allegations were reported in some sections of the media.
"These reports were made with no knowledge of the facts and created the impression that Bolton players were subjected to racial chanting or systematic abuse by more than one individual. We trust that, now the facts have emerged, certain individuals will reflect on their reports.
"Finally, it is our hope that all of us within football can continue to work together to build on the progress that has been made over many years in effectively tackling the issue of racism in our game."
FA supports Millwall action
The FA and Bolton both released statements expressing their satisfaction with the way the incident had been handled.
The FA said: "We applaud both Millwall FC and Bolton Wanderers FC for their commitment and cooperation in ensuring a full and thorough investigation could take place. The FA fully supports Millwall's approach in terms of dealing with the young individual responsible."
And Bolton said: "We would like to thank the FA and Millwall for their co-operation and assistance in responding to the events at The Den.
"Marvin Sordell would like to thank the FA, the PFA and Kick it Out for their support, and Millwall for the way in which they dealt with this."