The 61-year-old, who has had issues with drugs in the past, confessed he paid for two deliveries of the class A drug in the space of 14 hours.
But he's determined to get clean again. In a statement, Alexander, who quit the show after calling Perez Hilton a f****t, said: "It has been extensively reported how this series of CBB has been one of the most stressful and volatile in the history of the show."
The statement to the Sunday Mirror continued: "It has been documented in the past that Alexander has had issues that have led to him seeking professional help and treatment.
"This was a monetary relapse, completely out of his recent character and behaviour and he will certainly be addressing and dealing with this immediately."
R&B singer Alexander has been staying in a London hotel since leaving the house, and staff reportedly told the Mirror they could smell drugs being smoked in his room.
"Alexander has a lot of positive projects to look forward to over the next few months, including his tour and new material he is working on, and hopes this momentary lass will not interfere with those," the statement went on.
"He asks his fans to forgive him and apologises if he has let any of you down."