The General Medical Council has found Professor Sir Roy Meadow guilty of giving erroneous and misleading evidence in the Sally Clark case.
Sir Roy denies serious professional misconduct
GMC members are now considering whether this amounts to serious professional misconduct and if so what sanctions, if any, to impose.
Sir Roy has stood by his evidence, but admitted his use of statistics at Mrs Clark's 1999 trial was "insensitive".
Mrs Clark was convicted of murdering her two sons, but exonerated in 2003.
During the trial, Sir Roy said the probability of two natural unexplained cot deaths in the family was 73 million to one.
Sally Clark: Served three years after being wrongly convicted of killing her two sons
Angela Cannings: Served 18 months after being wrongly convicted of killing her two sons
Donna Anthony: Served six years after being wrongly convicted of killing her son and daughter
Trupti Patel: Cleared of killing three of her children
The figure was later disputed by the Royal Statistical Society and other experts have said that once genetic and environmental factors are taken into consideration, the odds are closer to 200 to one.
The GMC ruled on Wednesday that Sir Roy did not intend to mislead in evidence he gave at Mrs Clark's trial.
However, members of the disciplinary panel decided his overall evidence was misleading and that he "erroneously implied" that two deaths in a family would be independent of one another.
Mrs Clark was eventually freed after it become apparent that another witness at her trial, pathologist Alan Williams, had failed to disclose key medical evidence.
Putting the case for the GMC at the start of the hearing, Robert Seabrook QC said Sir Roy had been a pre-eminent paediatrician and child expert with many achievements during a long career.
However, he said he had been in breach of his duties as an expert witness in the Clark trial.
"He either didn't understand what he was doing, should not have given evidence and was incompetent to do so, or he was using the information carelessly in support of the proposition that Sally Clark smothered her babies."
Giving evidence, Sir Roy defended the calculations he used to arrive at the 73 million to one figure.
But he said he regretted comparing the odds of two cot deaths in the same family to that of a punter successfully backing an 80-1 shot at the Grand National four years in a row.
"The situation in which I was giving evidence was one in which there was a family grieving, two children had died and the mother had been accused of murder," he told the hearing.
"To raise a subject like the Grand National, that is exciting and vibrant, is insensitive and I should have thought of more appropriate odds."
Sir Roy also gave evidence as an expert witness in the trials of two other women, Angela Cannings and Donna Anthony, who were both freed on appeal after being convicted of murdering their children.
Speaking outside the hearing, Mrs Clark's father Frank Lockyer said: "No one is in any doubt that the evidence on which my daughter was convicted was seriously flawed.
"This hearing was first and foremost about culpability and accountability which seems to have been well and truly settled."
The hearing, which was adjourned until Thursday, heard testimonies from leading paediatricians in support of Sir Roy, who retains a great deal of respect within the medical profession.