President Enrique Pena Nieto had reacted crossly at the time to those who criticised the purchase, saying there were "countless versions and falsehoods" surrounding the story.
First lady Angelica Rivera also reacted angrily at the time, denying she had done anything wrong. She claimed she was using money she earned during her career as an actress.
But she later returned the mansion, which she had been paying for in installments.
Yesterday, Pena Nieto said he understood why Mexicans would be angry about the apparent conflict of interest.
Speaking at the presentation of a new anti-corruption law, Pena Nieto offered "my profound and sincere apology for the offence and indignation I caused."
"I personally felt the Mexican people's irritation, I understand it perfectly," Pena Nieto said. "For that reason, with all humility, I ask their forgiveness."
Just days before the news reports surfaced, Pena Nieto's government cancelled a high-speed rail contract that had been granted to the sole bidder, a consortium that included a division of the company that sold Rivera the mansion.
Mexico's Public Administration Department had said that neither the president nor his wife incurred any conflict of interest.
There will also be a measure of civilian oversight in the new system.
Eduardo Bohorquez, director of Transparencia Mexicana, called the new law a step forward, but said a lot would depend on how it was implemented.
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