He previously played in two stints for the Florida Panthers where he was originally selected 71st overall in the 2007 NHL Entry Draft, as well as the Ottawa Senators, Vegas Golden Knights and Montreal Canadiens.

[1] Dadonov was recalled by the Panthers and made his NHL debut on 6 April 2010 in a 5–2 loss to the Ottawa Senators, though the coach, Peter DeBoer praised his play after the game.

With his rights having expired from the Hurricanes, Dadonov returned to his original club, the Florida Panthers, in agreeing to a three-year, $12 million contract on 1 July 2017.

[15] After three productive seasons with the Panthers, Dadonov left the club as an unrestricted free agent, to sign a three-year, $15 million contract with the Ottawa Senators on 15 October 2020.

[15] Dadonov saw his production drop in his first season after signing with the Senators compared to his time in Florida, putting up 20 points in 55 games, under half a point-per-game average.

[16] After a disappointing first season with the Senators, Dadonov was traded to the Vegas Golden Knights in exchange for Nick Holden and a 2022 third-round draft pick on 28 July 2021.

[19] A report the same day stated the Golden Knights claimed the Senators did not inform them of the no-trade clause, and the NHL's central registry processed the trade before Dadonov disputed its validity.

[22] Dadonov's profile was elevated as a result of the events, and days after the resolution he scored the overtime-winning goal in a 26 March game against the Chicago Blackhawks, receiving strong applause from the audience.

[24][18] Following the Golden Knights missing the postseason for the first time in franchise history, Dadonov was traded to the Montreal Canadiens in exchange for Shea Weber on 16 June 2022.

[26] On 26 February 2023, Dadonov was traded by the Canadiens, with half his salary retained, to the Dallas Stars in exchange for fellow struggling Russian, Denis Gurianov.