The son of a fitter in a metal factory and a nurse, Tszyu was born in a town named Serov, near the Ural Mountains.
Tszyu and his family, including sister Olga, used to share an apartment with another family, and Tszyu used to sleep on the floor. Tszyu was hyperactive as a child, and his father decided to take him to a boxing gym, where he would channel that energy by fighting older boys. Soon, Tszyu impressed Russia's amateur team coaches and he was sent to the Soviet Union's amateur boxing travelling training camps, where he got to visit more than 30 countries while training and fighting in tournaments. He trained with that group 250 days a year, and won various tournaments, such as amateur boxing's world championships. He also participated in the Olympic Games. At the Cuban world championship tournament in 1987, he came in second place, and at the Seoul Olympic games, he lost in the third round.
Kostya was a member of the Soviet military too, but since he was selected as an elite athlete, he did not have to participate in any wars.
He fought at the world championships once again, in Moscow in 1989, where he came in third place.
In 1991, he went again to the amateur world championships, this time held in Sydney. This was a trip that would change his life forever. Not only was the third time his charm, but he felt enchanted with the sights of Sydney and its people, and decided he wanted to live in Australia.
After the collapse of the Soviet Union, in 1992, Tszyu escaped from the Russian army and fled to Australia with his girlfriend, where they married in 1993 and became Australian citizens. Before marrying her, though, Tszyu had already turned professional, beating Darrell Hiles by a knockout in one round on March 1, 1992 at Melbourne.
Tszyu started raising his quality of opposition almost immediately. In his fourth professional bout, he met the former WBC Featherweight champion of the world Juan Laporte, decisioning him over ten rounds. In his sixth bout, he beat the future WBO junior welterweight champion of the world Sammy Fuentes by a knockout in the first. In 1993, Steve Larrimore, Larry La Crousiere and Robert Rivera, all fringe contenders, went to Australia to fight Tszyu, and none lasted more than two rounds. The only man to last more than two rounds with Tszyu in '93 was Livingstone Bramble, a former world Lightweght champion, who lost by decision to Tszyu at Newcastle, Australia.
In 1994, Hector Lopez, who would later challenge Fuentes for the world title, Angel Hernandez, who had just come off challenging Julio Cesar Chavez for the WBC belt and Pedro Chinito Sanchez, a fringe contender from the Dominican Republic tried to beat Tszyu, but Tszyu beat Lopez by a decision in ten, Hernandez by a knockout in seven, and Sanchez by a knockout in four. After the win against Sanchez, Tszyu was ranked number one in the Jr. Welterweights.
And then, in 1995, he received his first world title shot, when he fought IBF world junior welterweight champion Jake Rodriguez at Las Vegas, Nevada. Tszyu became world champion by knocking Rodriguez out in the sixth round, and then defended the world title beating former world junior lightweight and junior welterweight champion Roger Mayweather by a decision in 12, Hugo Pineda by a knockout in 11, Cory Johnson by a knockout in four, and Jan Bergman by a knockout in six. After that string of defenses, Tszyu became a highly touted world champion by many boxing magazines, and many articles about him appeared on Ring Magazine, KO Magazine, and other American boxing publications.
1997 began for Tszyu when his defense against Leonardo Moro Mas was declared a no contest because Mas' camp protested that the blow that finished their fight in the first round was actually a low blow. Undecided whether it was a low blow or a legal blow, the IBF and the Nevada State Athletic commission decided to declare it a no contest instead. For his next bout, however, Tszyu wasn't as lucky, and he lost for the first time, losing by a knockout in ten rounds to Vince Phillips, who also took with that, Tzsyu's world championship. He regrouped after that defeat, and came back to beat Ismael Chaves just before year's end.
After beating former world champions Calvin Grove (KO2) and Rafael Ruelas (KO9), Tszyu was given another world title try, when the WBC's belt became vacant in 1998 following Oscar De La Hoya's move to the Welterweight division, and Tszyu found himself twice on the canvas in round one of his fight for the vacant belt against Diobelis Hurtado, but recuperated to beat Hurtado by a knockout in five and become world champion once again. He retained the title once in 1999, knocking out former world champion Miguel Angel Gonzalez in ten, and twice in 2000, beating Arizona's fringe contender Ahmed Santos in eight, and Mexican legend Chavez, the former world champion, in six at Phoenix, Arizona.
Then, he started talking about his wish to unify all the belts. In 2001, he began that quest by facing the WBA's world champion Sharmba Mitchell and taking the WBA belt from Mitchell by a knockout in seven. After that, he met another Russian, Oktay Urkal, whom he beat by a 12 round decision after 12 rounds. Finally, he finished 2001 by recovering his IBF belt in an unification bout with the until then IBF world champion Zab Judah, who was knocked out in two. A small melee inside the ring followed that fight, because Judah thought that the fight had been stopped early and he got mad at the referee, throwing his corner's seat at him. By then, however, Tszyu was long gone and in his dressing room. That win was chosen by Ring Magazine as their "Knockout of the Year".
Tszyu in 2002 had only one bout, beating fringe contender Ben Tackie of Ghana by a decision in 12.
On January 19 of 2003, Tszyu began the year by retaining his title against former world champion Jesse James Leija by a knockout in six. After the fight, held in Melbourne, Tszyu announced that fight could be his last in Australia because promoters want him to fight more in the United States. The win against Leija came on the birthday of Tszyu's son.
His immediate plans for 2003 include defending his title various times. He has been trying to get in the ring again with Phillips, and he also tried to fight with WBO world champion Demarcus Corley, but negotiations towards those two fights have not been successful for the moment, and became more complicated when Phillips lost to Ricky Hatton and Corley lost his title to Judah.
His record currently is of 30 professional wins (of which 25 were by knockout), one loss and one no contest.
He is considered by many in Australia to be a national sports hero.