In October the 38-year-old Harrison knocked out Scott Belshaw to win the Prizefighter heavyweight tournament.
BBC: Audley Harrison faces Michael Sprott for European title
Rogan won the heavyweight Prizefighter tournament earlier this year and is unbeaten in 11 bouts.
There have been seven previous Prizefighter events but Williams will be the first current British champion to participate.
"Audley is realistic and he sees this as his last chance, " Prizefighter promoter Barry Hearn told BBC Sport.
Scott's great-grandfather, Richard (Doc) Farmer, a circus prizefighter, collected chemical-soaked rags from factories and washed and returned them for a fee.
Once upon a time there was a prizefighter named Cassius Clay who changed his faith and his name, to Muhammad Ali.
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Rogan, 37, achieved some notoriety by winning the recent heavyweight 'Prizefighter' tournament at London's York Hall and is unbeaten in paid 10 fights.
His father had been, among other things, a prizefighter at country fairs, more or less on the wrong side of the law all his life.
He last fought when winning the Prizefighter heavyweight tournament last October.
Hearn believes events like Prizefighter, with quarter-finals, semis and final staged over a single evening, can be a shot in the arm for a sport he loves.
This is not, however, like paying for training a prizefighter.
"Prizefighter has brought boxing back to the people, " said Hearn.
And that could come in the form of Prizefighter promoter Barry Hearn, who told BBC Sport after Friday's victory that he is trying to arrange a deal with Harrison.
However, Harrison, who won promoter Barry Hearn's Prizefighter tournament last October to keep his career afloat, admitted that defeat to his Polish opponent at Alexandra Palace would end his career.
Harrison won gold in the super-heavyweight division at the Sydney Olympics, but four defeats in eight fights left his career in the balance before Prizefighter offered him a route back.
The 1998 Commonwealth Games champion reignited his career by winning Prizefighter last year and then scored a 12th-round knockout against Michael Sprott to win the EBU heavyweight title in April.
Prizefighter has evolved and resurrected my passion for boxing.
Prizefighter has been growing with each event and moving the night from Bethnal Green's York Hall to the 5, 000 capacity ExCel Arena in Docklands because of ticket demand is testimony to this.
Yes, Harrison won Friday's Prizefighter event and rightly told BBC Sport when asked about the quality of opponent that all he can do is "beat the men put in front of me".
And while the reception was slightly more forgiving for the Londoner after disposing of Belshaw, then Danny Hughes and finally Coleman Barrett to claim victory in the latest Prizefighter series, his doubters remain.
Barrett's victory set the tone for a night of upsets at Prizefighter, a contest that saw eight heavyweights compete in a succession of three-round bouts, beginning with four back-to-back quarter-finals, followed by semis and a final.
And Harrison, who has now lost four times in his 27-fight career, including a points defeat to previous Prizefighter champion Martin Rogan last December, knows that anything other than victory will be the final nail in his coffin.
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