Dobkin was born into a Jewish family in Kharkiv. He graduated from the National University of Internal Affairs (degree in law) and Kharkiv National Economic University (majoring in international economics).
From 1993 till 2002 Dobkin was an entrepreneur and director of several businesses.
In his 2015 tax declaration Dobkin stated that he owned 12 luxury cars.
In the 2002 Ukrainian parliamentary election Dobkin was elected People's Deputy of Ukraine. First he was a member of the faction of For United Ukraine, later in the faction of Social Democratic Party of Ukraine (united) (he was a member of this party) and ended his legislature in the faction of Party of Regions. Since late 2005 Dobkin is a member of the political council of Party of Regions.
From March 2006 to March 2010 Dobkin was Mayor of Kharkov.
In March 2010 President Viktor Yanukovych appointed Dobkin Governor of Kharkiv Oblast.
In 2014, he formed a "Ukrainian Front" organisation, in support of President Viktor Yanukovych, stating the intention to "clean and purify our Ukrainian land of those who come here with plans for occupation." In February 2014, Dobkin called for Ukraine’s capital to be moved from Kiev to Kharkiv, and for a federal structure of government to be established in Ukraine. He also claimed that by late February 2014 "all peaceful protesters of Euromaidan had left" and that with the remaining protesters "Negotiations with them will be to no avail. They need to disarm, and those who resist and kill people physically destroyed".
After Yanukovich was forced out of power Dobkin was a major participant in a meeting of local officials in Eastern Ukraine which questioned the legality of the new government's actions and declared local officials would take responsibility for their own regions until order was restored. Dobkin was later reported to have fled to Russia along with the mayor of Kharkiv Gennady Kernes, but he returned to attend a pro-Russian rally in the city. Late February 2014 he indicated that he intended to run for president in the upcoming Ukrainian presidential election due to his concerns regarding the behavior of the revolutionary government towards the Russophone population. Dobkin tendered his resignation as governor on 26 February 2014 "following my decision to run for the office of the President of Ukraine". On 2 March 2014 a decree by acting President Oleksandr Turchynov formally dismissed Dobkin.
On 10 March 2014 Dobkin was arrested on charges of leading a separatist movement. On 20 August 2014 "in the absence of corpus delicti" Dobkin's criminal case was closed.
On 25 March Dobkin filed documents to the Central Election Commission to run for presidency. On 29 March a Party of Regions convention supported Dobkin's nomination as a presidential candidate. During the election campaign Dobkin advocated a federalization of Ukraine's oblasts, Ukraine joining the Customs Union of Belarus, Kazakhstan and Russia, "rapid restoration of friendly and partnership relations with Russia, as well as the creation of a common humanitarian space", "defending the joint Russian-Ukrainian history, culture and traditions", maintaining Ukraine's neutral status, tax relief in the agricultural sector over the next 15 years and the formation of an army purely on contract basis. In the 2014 Ukrainian presidential election he received 3.03% of the vote, ranking 6th among all candidates.
In the October 2014 Ukrainian parliamentary election Dobkin was again re-elected into parliament; this time after placing third on the electoral list of Opposition Bloc.
On 13 July 2017 the Ukrainian parliament stripped Dobkin of his parliamentary immunity. He is suspected of abuse of office and assistance to fraud in order to get ownership of 78 hectares of land in Kharkiv worth more than $8.5 million. Two days later a Kiev court ruled Dobkin should be remanded in custody until 14 September 2017 and granted bail at 50 million hryvnia (at the time about US$1.9 million). On 19 July, members of the Opposition Bloc posted his $1.9 million bail.
Dobkin is married and has three children; a son and two daughters.
Since they met in 1998 Dobkin is a close friend of Mayor of Kharkiv Gennady Kernes.
Dobkin's younger brother Dmytro Dobkin is since the 2012 parliamentary election People's Deputy of Ukraine for the Party of Regions. And since the 2014 parliamentary election for Opposition Bloc.
Dobkin is widely known as "Dopa".