Ms Fyles was selected by Labor's 14-member caucus on Friday following days of behind-the-scenes wrangling between the party's left and right factions.
"This morning the caucus has selected me as the unanimous choice for leader of the Territory Labor Party," Ms Fyles said in a statement.
She will be sworn in as chief minister by the territory's administrator later on Friday.
Ms Fyles, from the left faction, is the second woman to be appointed chief minister and the third to lead Territory Labor.
She is also the second of the NT's 12 chief ministers to be born in the territory since the Legislative Assembly's first election in 1974.
No one publicly nominated for the top job but it was expected to go Mr Gunner's right-aligned deputy, Nicole Manison.
Former health minister Ms Fyles, 43, was viewed as her likely deputy.
Former union boss and AFL player Joel Bowden is also understood to have expressed an interest in the top job from the back bench but his left-faction challenge faded on Thursday.
Mr Gunner, 46, stood down on Tuesday moments after handing down the NT budget, saying his head and heart were no longer in the job.
Ms Fyles, a former schoolteacher and mother of two boys, entered parliament in 2012.
A media conference will be held later in the day.
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