Ledger, 28, was found dead last week in his Manhattan apartment. The cause of his death is expected to be determined after toxicology tests are completed.
The latest issue of Us Weekly cites a source who had been close to Ledger as saying the "Brokeback Mountain" star abused alcohol, cocaine, heroin and a "variety of pills," during the course of his three-year relationship with Williams, the mother of his 2-year-old daughter, Matilda.
The magazine said Williams was so distraught by Ledger's substance abuse, she drove him to the Promises Treatment Center in Malibu, Calif., in March 2006, however, he refused to go in and promised her he would get sober.
The couple broke up in September 2007 and Us Weekly said two sources told it Williams insisted Ledger undergo drug tests before his visits with Matilda.
An insider on the Swedish set of Williams' latest movie "Mammoth' said the actress "cried and screamed as soon as she heard" Ledger had died.