Sources familiar with the situation told the website that Sheen and Richards signed a written agreement stating that Richards now has sole legal custody of Sam, 6, and Lola, 4. The two previously had joint legal custody of the girls.
According to the report, the sources said that Richards wanted sole custody, given Sheen's recent "marital turmoil, sobriety issues and criminal problems," and that Sheen did not put up a fight about signing the agreement.
TMZ said the agreement was signed two weeks ago but that Richards and Sheen didn't want to file it with the court just yet.
With full legal custody, according to the report, Richards can now make medical and school-related decisions without Sheen's input. She can also leave the country with the children without his permission.
Sheen and Richards divorced in 2006. Under their divorce agreement, Richards has primary physical custody and Sheen has visitation rights.
The actor is grappling with legal problems arising from a fight with his current wife, Broke Mueller, in Aspen, Colo., last December. He is charged with assault, criminal mischief and menacing, which carries a possible sentence of one to three years in prison. He pleaded not guilty on March 15 and a trial is scheduled for July 21.
He and Mueller have twin 1-year-old sons, Bob and Max.
In February, Sheen entered a rehab facility for undisclosed treatment, temporarily forcing "Two and a Half Men" to halt production.