Williams’ reward for his stunning July knockout of Mike Tyson is a December 11 trip to New York to face reigning WBC champion Vitali Klitschko.
The pair are expected to meet at Madison Square Garden although final contracts for the venue will not be completed until next week.
Williams admitted his life had changed since the win in Louisville which catapulted him onto the world stage.
But freed from the self-doubt and pressure which blighted his early career, Williams insisted he would take advantage of his transformation to reach the top.
The Brixton 31-year-old said: “This fight is something I have been dreaming about since I was eight years old.
“Even after beating Mike Tyson I didn’t realise that a shot at the real world heavyweight title would come along so quickly.
“I have been watching Joe Louis, Rocky Marciano and Muhammad Ali on videos and for me to be fighting for the same title is amazing.”
The former British champion said he never doubted he would one day compete on the biggest stage despite a number of well-documented setbacks.
His big chance appeared to have gone for good in February 2003 when he was smashed to a sixth-round defeat by Sinan Samil Sam in a European title challenge.
And as recently as January this year Williams dropped a dismal points decision in a British title defence against Michael Sprott.
But Williams insisted: “I never doubted for a moment that one day I would get there - my only surprise is that it has come so quickly.
“I used to put a lot of pressure on myself. But once I got over that stress I stopped getting pressure and my career went from strength to strength.”
Klitschko, said Williams, was the clear favourite for his first defence of the title he claimed against Corrie Sanders after Lennox Lewis’ retirement. The big Ukrainian was ringside on Williams’ glory night in Louisville and pronounced himself impressed - not to mention disappointed - with what he saw.
Klitschko said: “I wanted Williams because he destroyed my dream of fighting Mike.
“I was very close to doing that and I was disappointed, but I was also surprised and impressed with Williams’ performance.”
Klitschko is generally regarded as the number one heavyweight champion after pushing Lewis until a controversial cuts stoppage in their fight in June last year.
He remains bitter about the circumstances of that defeat and not least Lewis’ subsequent decision to retire without granting a much-hyped rematch.
Klitschko added: “Everybody knows Lewis retired because I sent him into retirement.
“I can say I have already beaten two British fighters - Herbie Hide in London in 1999 and Lewis in Los Angeles last year.”
Klitschko is far too intelligent to take Williams for granted, with the challenger’s trainer Jim McDonnell determined to send him into the ring in even better shape.
McDonnell added: “Danny will be in the same shape in one week’s time as he was for the Tyson fight.
“We are taking Danny’s training to a different level this time and it is going to pay off when he becomes world heavyweight champion in December.”