Zadorov played in the 2008 Quebec International Pee-Wee Hockey Tournament with the HC CSKA Moscow youth team. He played in the top minor hockey level with his hometown team in Moscow, Krasnaya Armiya, in the 2011–12 season. Showing unique agility and skating prowess for a formidable frame, Zadorov scored 6 points in 42 games. He was selected by affiliate Kontinental Hockey League club CSKA Moscow in the first round, fourth overall, of the 2012 KHL Junior Draft. However, with an impressive performance with the junior national U17 team in Windsor, Ontario, and stating his intention to pursue a career in North America in order to be selected in the NHL draft, London Knightsgeneral managerMark Hunter traded up with the Peterborough Petes in the 2012 CHL Import Draft to select Zadorov ninth overall. After agreeing to a contract with the Knights, Zadorov began his major junior career in the Ontario Hockey League in the 2012–13 season. Joining fellow Russian Vladislav Namestnikov and after adapting to the differing style and dimensions of the North American game, Zadorov assumed a top pairing role and led All-Rookie defenceman in plus–minus with +33, and finishing second in scoring with 6 goals and 25 points in 63 games. Earning a roster spot in the 2013 CHL Top Prospects Game, Zadorov helped the Knights claim the OHL championship to advance to the Memorial Cup. As he was selected to the OHL First-All Rookie Team, he scored the game-winner in the opening game against the Western Hockey League's Saskatoon Blades before losing in the semi-finals. Zadorov's impressive season was noted as he was selected with the Buffalo Sabres's second first-round pick, 16th overall, in the 2013 NHL Entry Draft.
Buffalo Sabres
Zadorov attended his first rookie and NHL training camp and after his third pre-season contest he was signed by the Sabres to a three-year, entry-level contract on 26 September 2013. Under the assessment of head coach Ron Rolston, he made the Sabres' opening night roster to begin the 2013–14 season. Zadorov sat out the first ten games before he made his NHL debut in a 4–2 defeat to the Colorado Avalanche on 19 October. In just his second game, against the Boston Bruins on 23 October, Zadorov scored on his first shot in the NHL, against Chad Johnson. In so doing, he became the youngest Sabres defenceman in franchise history to achieve the feat. With the Sabres cleaning out the front office and coaching staff, and with an imperative to rely less on the youth from new head coach Ted Nolan, on 19 November, Zadorov was returned to junior with the London Knights after seven NHL games played. He played out the remainder of the season with the Knights, assuming a top-pairing role in surpassing his rookie season totals in points in half the number of games, earning a selection to the OHL Second All-Star Team. Despite a benching during the rookie pre-season tournament in Traverse City, Michigan, Zadorov rebounded to have a strong training camp to make the Sabres' opening-night roster in the 2014–15 season as a permanent addition to the blueline. He initially only saw limited playing time as a rotational option to the third-pairing under Ted Nolan and was primarily on the team for practice only. Zadorov's playing time soon increased in the season as the team's coaching staff decided to keep Zadorov regardless of his junior situation. In developing a shut-down role through his physicality, Zadorov showed offensive glimpses, collecting his first multi-point game in scoring an overtime marker in a 4–3 victory over the Florida Panthers on 13 December 2014. Zadorov also became the youngest Sabres defenceman in history to score an overtime winner. Zadorov showed his youth by suffering two team suspensions over the course of his rookie campaign, after returning late from holiday over the All-Star break and later oversleeping through a team practice. Despite a lowly year for the Sabres, Zadorov led the blueline in plus–minus and finished with 3 goals, 12 assists in 60 games.
Colorado Avalanche
At the 2015 NHL Entry Draft, Zadorov was traded as a central piece by the Sabres in a package that also included Mikhail Grigorenko, J. T. Compher and the 31st pick in the draft to the Colorado Avalanche in exchange for Ryan O'Reilly and Jamie McGinn on 26 June 2015.
Zadorov married his wife Aleksandra Zadorova on June 12, 2015. Their 2 year-old daughter, Sophie, was born on April 12, 2017. The family also has a west highland white terrier named Luna.