This from Dale Nelson, of Mayville State University:
According to Michael Slater’s Charles Dickens: A Life Defined by Writing (2009, p. 502), Dostoevsky talked with Dickens in London at the office of All the Year Round in summer 1862. Dostoevsky wrote about the meeting to Stepan Dimitriyevich Yanovsky in a letter dated 18 July 1878, so 16 years after the event. The letter was translated by Stephanie Harvey in Dickens’s Villains: A Confession and a Suggestion, published in The Dickensian vol. 98 (2002): 233-5.
The Dostoevsky passage, as quoted by Slater:

—He told me that all the good simple people in his novels, Little Nell, even the holy simpletons like Barnaby Rudge [!?], are what he wanted to have been, and his villains were what he was (or rather, what he found in himself), his cruelty, his attacks of causeless enmity towards those who were helpless and looked to him for comfort, his shrinking from those whom he ought to love, being used up in what he wrote. There were two people in him, he told me: one who feels as he ought to feel and one who feels the opposite. From the one who feels the opposite I make my evil characters, from the one who feels as a man ought to feel I try to live my life. Only two people? I asked.—

I would be happier if Dostoevsky had written the letter right after the interview. I figure, though, that, at the least, these two did actually meet. That seems wonderful.
Update: The story of the Dostoevsky-Dickens meeting is a hoax. See the Comments for more details.