In 2004, Lebedev won the vacant Russian light heavyweight title in a shut out 10-round decision win against Artem Vychkin.

[7] The fight, a 10-round bout, which was billed as the “Battle of Two Empires” was announced to take place on 22 May at the Krylatskoye Sports Palace in Moscow.

The final punch put Jones out cold on the canvas and he did not regain his senses for more than 5 minutes amid active medical help.

[17] The fight was rescheduled to take place on 4 November at the Khodynka Ice Palace in Moscow over 12 rounds for the interim WBA cruiserweight title.

Although Toney still possessed enough defensive skills, Lebedev dominated the fight from the start winning a lopsided decision with scores of 120–108, 120–108 and 120–108.

[20][21] Lebedev made his first defence of the interim world title at the Crocus City Hall in Myakinino, Russia, on 4 April 2012 against Shawn Cox.

[22] In round 2, Cox threw a straight right hand which missed, and walked into a Lebedev counter power left hook to the head, knocking him out.

[28] In October, Jones was stripped for backing out of his scheduled WBA title defense against challenger Andres Taylor and then refusing to fight Lebedev.

[29] On 16 November, it was announced that Lebedev would fight undefeated Colombian boxer Santander Silgado (23–0, 17 KOs) at the City Hall on 17 December 2012.

[41] Two weeks after the fight, Lebedev demanded a rematch with Jones, likely for the Wladimir Klitschko vs. Alexander Povetkin undercard in October.

[43][44] Jones was stripped of his title later in the year for failing a drug test for this fight, resulting in Lebedev being reinstated as Champion by the WBA.

[49] By the end of July, a fight between Lebedev and Kolodziej for the WBA title was confirmed to take place on 27 September at the Dynamo Palace of Sports in Krylatskoye, Moscow.

[50] In round 2, Lebedev floored Kolodziej with a well timed power left hook to the face retaining his WBA cruiserweight title.

[55] On 16 March, a day before the scheduled purse bids, a deal was reached for Lebedev vs. Kalenga to take place on 10 April at the Luzhniki Palace of Sports in Russia.

[58] On 18 August 2015, Ringtv announced that Lebedev would defend his WBA title against undefeated Nigerian boxer and friend Lateef Kayode at the Tatneft Arena in Kazan, Russia on 4 November.

[59][60] Lebedev retained his world title after knocking Kayode down three times in the bout before the fight was eventually stopped by the referee.

"[61] It was announced that Lebedev would be involved in a cruiserweight unification fight against IBF world champion Victor Emilio Ramírez at the Khodynka Ice Palace in Moscow on 21 May 2016.

The power shots continued from Lebedev until referee Steve Smoger stopped the fight, although giving Ramírez every chance to get back into the bout.

[64] It was announced in August 2016, that a fight between Lebedev and unbeaten IBF #1 challenger Murat Gassiev (23–0, 17 KOs) was in the works for November or December.

Gassiev became the mandatory challenger by the IBF after knocking out American boxer Jordan Shimmell in a title eliminator bout in May.

[70] Lebedev knocked Flanagan down in round 9 with a left hook to the body and went on to win a lopsided unanimous decision with the judges scoring the fight 119-108, 120-107 and 119-108 all in his favour.

Although Flanagan showed heart in recovering well, had little chance overcoming the experienced champion, only winning a round on two judges scorecards.

[71] On 1 February 2018, the WBA demoted Lebedev to 'champion in recess' and promoted Cuban Yuniel Dorticos from 'regular' to 'full' champion in order for his WBSS semi final fight with IBF beltholder Murat Gassiev to be a true unification.

[72] On 21 July, Oleksandr Usyk defeated Murat Gassiev to become the undisputed cruiserweight champion, holding all four major belts.

A day later, promoter Andrei Ryabinsky was discussing the possibilities of Lebedev using his status as 'champion in recess' to force a fight with Usyk.

His promoter Dmitriy Salita said, “Alexey’s skills, size drive and determination make him a big threat in the cruiserweight division.

In this fight particularly Alexey is very hungry to break into the scene with the best cruiserweights in the world.”[75] German-based Turkish boxer Hizni Altunkaya (30-2, 17 KOs) was confirmed as Lebedev's opponent in a scheduled 10 round bout at the Traktor Sport Palace.

Altunkaya was last seen in action, losing via TKO against a returning Beibut Shumenov for the vacant WBA (Regular) title in July 2018.

Lebedev struggled to cut off the ring in the opening round as Altunkaya was able to use his foot movement to avoid any damage.

[82][83] On 21 December 2019, Lebedev, ranked #9 by the WCB at cruiserweight, fought WBC #8 and IBF #15 Thabiso Mchunu in his home country of Russia.