Tartakovsky was born Gennady Tartakovsky (Russian: Геннадий Тартаковский) on 17 January 1970, in Moscow, to Jewish parents. His father worked as a dentist for government officials and the Soviet Union national ice hockey team. Genndy felt that his father was a very strict and old-fashioned man, but they had a close relationship. His mother, Miriam, was an assistant principal at a school. He has a brother, Alexander, who is two years older and a computer consultant in Chicago. Before coming to the United States, his family moved to Italy. There, Tartakovsky was first drawn to art, inspired by a neighbor’s daughter. Tartakovsky later commented, “I remember, I was horrible at it. For the life of me, I couldn’t draw a circle”.

Tartakovsky created the action-adventures series Samurai Jack, which premiered in 2001; he also wrote comics for the franchise. The series won him an Emmy in the category of “Outstanding Animated Program (For Programming Less Than One Hour)” in 2004. Star Wars creator George Lucas hired Tartakovsky to direct Star Wars: Clone Wars (2003–2005), an animated series taking place between Attack of the Clones and Revenge of the Sith. The series won three Emmy awards: two for “Outstanding Animated Program (for Programming One Hour or More)” in 2004 and 2005, and another for “Outstanding Individual Achievement in Animation” (for background designer Justin Thompson in 2005). Tartakovsky was not involved in the 2008 follow-up series.

In 2005, Tartakovsky was appointed creative president of Orphanage Animation Studios. In 2006, he was chosen as the director for a sequel to The Dark Crystal, but was replaced and the film was later scrapped. Tartakovsky served as animation director on the pilot episode of Korgoth of Barbaria, which aired on Adult Swim in 2006 but was not picked up as a series. He also directed a series of anti-smoking advertisements, one for Nicorette in 2006 and two for Niquitin in 2008. In 2009, Tartakovsky created a pilot entitled Maruined for Cartoon Network’s The Cartoonstitute program, which was not picked up.

In 2009, it was announced that Tartakovsky would write and direct a Samurai Jack film from Fred Seibert’s Frederator Studios and J. J. Abrams’ Bad Robot Productions. In June 2012, Tartakovsky said that he had a story to conclude the series and title character’s story, but the project had been shelved after Abrams moved on to direct Star Trek. In 2010, Tartakovsky created storyboards for Jon Favreau’s Iron Man 2. He created a new series for Cartoon Network, Sym-Bionic Titan, between 2010 and 2011. He had hoped to expand on the initial season, but it was not renewed. On 7 April 2011, an animated prologue by Tartakovsky for the horror film Priest premiered online.

In early 2011, Tartakovsky moved to Sony Pictures Animation, where he made his feature film directing debut with Hotel Transylvania (2012). In July 2012, he signed a long-term deal with Sony to develop and direct his own original projects. In June 2012, Sony announced that Tartakovsky was slated to direct a computer-animated Popeye feature. On 18 September 2014, Tartakovsky revealed an “animation test”. In March 2015, Tartakovsky announced that despite the well-received test footage, he was no longer working on the project. He moved onto directing original story Can You Imagine?, announced in 2014, but it was cancelled.

Tartakovsky directed Hotel Transylvania 2, the sequel to Hotel Transylvania, released in 2015. In December 2015, Adult Swim announced that Tartakovsky would return for a final season of Samurai Jack, during which he stepped away from Sony Pictures Animation. When the series finished airing in 2017, Tartakovsky returned to Sony and directed Hotel Transylvania 3: Summer Vacation (2018). After its financial success, two original projects were announced: an R-rated comedy called Fixed and an action-adventure film entitled Black Knight.

In May 2019, it was announced that Adult Swim had commissioned a new series from Tartakovsky entitled Primal, which is about “a caveman at the dawn of evolution … [and a] dinosaur on the brink of extinction”. It began airing on 7 October 2019.

On 11 May 2020, it was announced that Tartakovsky’s Popeye project was being revived by King Features Syndicate, with T. J. Fixman writing the script. Tartakovsky later clarified that he was not working on it yet and funding was still needed, saying that if he had the time he would do it.

Tartakovsky was involved in the development of the video game Samurai Jack: Battle Through Time, which was released on 21 August 2020. On 28 October, a new series by him called Unicorn: Warriors Eternal was announced; it will focus on a group of teen heroes, drawing inspiration from world mythology, and is being billed as all-ages animation. It is being produced by Cartoon Network Studios to be aired on Cartoon Network and HBO Max as part of an attempt by WarnerMedia to reach a broader range of the “older kid and tween market.”