"Hekkie is in the best shape of his career," Nathan said.
"This is a fight he has dreamt about for years, and [he] is doing everything possible to provide the best performance of his career."
Golden Gloves promoter Rodney Berman has revealed that the bout will be for the highest purses ever paid to two South African boxers at this particular weight level.
Many of the fighters on the June 15 bill went through their paces at an enthusiastically attended public work-out at Nathan's "Hot Box" gym on Tuesday afternoon.
It was initially believed that the long-awaited fight between Budler and Joyi would not materialise, because of a rift between the rival promoters who controlled their affairs.
Joyi, who was considered South Africa's number one pound-for-pound fighter before he surrendered his IBF title last year in a shock defeat, was one of the boxers not present at Tuesday's session.
He is respected world-wide, and at one stage Joyi was ranked as the number one straw-weight boxer in the world by the respected Ring Magazine.
"Nkosinathi Joyi was my hero and I expect I will go into the ring as the underdog," Budler said.
"I have long dreamt about being given the chance to meet him. He is not only a classy boxer, he has a killer punch as well, but I will do my damn best, and I truly believe that with all the effort I will put into this fight, I can beat him as well."
Between them, Joyi and Budler have fought 45 times, with each suffering a solitary defeat.
"Hekkie has a mountain to climb, but we are working on a blueprint to beat Joyi. It has happened in the past and it can happen again," Nathan said.
Heading the undercard on the bill is a return match-up between South Africa's IBO junior bantam-weight champion Gideon Buthelezi and Filipino Edrin Dapudong.
Buthelezi controversially received a negative points verdict when he fought Dapudong for the IBO title at Emperors Palace last year.
The IBO called for a rematch and Buthelezi will now have the chance to show he is indeed a worthy champion.
Golden Gloves announced a rematch for the all-Africa light-heavyweight title between Rayno Liebenberg and Johnny Muller.
However, Liebenberg said he was wasting his time fighting Muller again.
"This time I will not waste time and will make sure of an early knock-out," he said.
In a surprise announcement, Nathan revealed he had cut his ties with Jason Bedeman, and as a consequence Bedeman was removed from the tournament.