The singer's parents established The Amy Winehouse Foundation after her passing last year (11) in a bid to educate young people about substance abuse.
Anderton, who was once hooked on cocaine and became a high-priced hooker to pay her drug debts, has now revealed she has been supported by the scheme in her quest to quit cigarettes.
The star also admits that growing close to Winehouse's father Mitch has made her realise the heartache she put her own parents through as she battled her demons.
Anderton tells Britain's The Sun newspaper, "I stubbed out my last (cigarette) three months ago. Thanks to the support of Mitch, my family and amazing friends, I am finally completely clean of addiction.
"Mitch told me about Amy. He told me some beautiful stories about their relationship and had me in tears. I immediately called my mum and told her how sorry I was for putting her through hell for so many years.
"Speaking to Mitch about losing Amy really hammered home how hard it must have been for my parents and that if I hadn't been so lucky, I could be dead. Addiction is such a selfish disease. I hadn't given my family a second thought."
Anderton now works with the foundation to help troubled youngsters and adds, "I will be going around secondary schools... speaking to kids about the dangers of taking drugs.
"There is no detail I will hold back on if it means I'll be saving other families from the distress associated with addiction. I don't recognise the person I was all those years ago but I've forgiven myself now - addiction is a disease. I hope that by being honest about what happened to me it will make others think twice about dabbling in drugs."