Mr Williams, 37, died in a violent attack in September last year, leaving his family devastated.
Nicholas Bridge, 18, and Daniel Onofeghare, 20 were found guilty of killing him following a three-week trial in June.
Bridge, from Brixton, was found guilty of murder.
Onofeghare, of no fixed address, was found guilty of manslaughter by majority verdict.
How did this happen? Click here to watch our video looking back at the events of that tragic night.
They appeared at Brighton Crown Court this morning for sentencing.
Judge Jeremy Gold QC told the court: “Tony Williams was a much-loved family man.
“This was a merciless, premeditated killing.”
Speaking to Bridge, he said: “You attacked Tony Williams with ferocity.
“You inflicted a number of deep wounds to his abdomen and sadly I have no doubt that you intended to kill him and you succeeded in doing so.”
The court heard how in September last year Bridge and Onofeghare had become involved in selling Class A drugs on the streets of Horsham.
Judge Gold said: “You were running what had become known as a ‘county line’ from London, using addresses of vulnerable drug addicts in Horsham to supply local users, a form of activity known as ‘cuckooing’.”
He said there was ‘some evidence’ that Anthony was involved in a theft or robbery of drugs and/or money the night before his death.
He added: “You Onofeghare contacted Bridge who came to Horsham that following day to deal with the situation.
“You made enquiries as to Tony Williams’ whereabouts and that led you quickly through the local drug community to the flat in Horsham where Tony Williams was with other drug users.
“The two of you both went to that flat armed with knives.”
Judge Gold told the court how Bridge stabbed Anthony a number of times.
“He frankly had no chance, bearing in mind the ferocious hunting-style knife with which you were hurting him.
“Mr Onofeghare your role was to make sure that nobody in the flat stood in his way or tried to help Tony Williams.”
Sentencing Bridge, he said: “Sadly you stand before me just 18 years of age.
“I bear in mind particularly your youth, but at the end of the day this was a merciless, premeditated killing.”
Bridge was sentenced to a minimum of 24 years imprisonment.
Turning to the second defendant, judge Gold said Onofeghare did not share Bridge’s intention to kill or cause grievous injury to Anthony.
However he told Onofeghare he believed ‘without hesitation’ that he posed a risk to the public and therefore qualified for an extended sentence.
He was sentenced to 15 years detention in a young offenders’ institution, with an additional five years’ on licence upon his release.
Onofeghare was told he would serve at least two thirds of the 15-year period, before potentially being released on licence.
Between them, their sentences add up to 39 years.