Steiner, 58, had been in charge of the team since it entered F1 in 2016 and has attracted much attention for his lively outbursts on the successful Netflix show 'Drive to Survive'.
"It's disappointing and sad not being a part of the team going forward, but I wish the team all the best for the future. If any team deserves success, it's them. I will always root for Haas," said Steiner on X.
Team owner Gene Haas said: "I'd like to start by extending my thanks to Guenther Steiner for all his hard work over the past decade and I wish him well for the future."
But he added: "Moving forward as an organisation it was clear we need to improve our on-track performances."
Since joining F1, Haas has never succeeded in making the podium, Romain Grosjean's fourth place in Austria in 2018 proving to be their best finish.
Last season Nico Hulkenberg and Kevin Magnussen collected 12 points between them as Haas finished 10th and last in the constructors' championship.
Magnussen posted on X: "Thanks, Guenther. Thanks for taking me on the journey in 2017 and thanks for bringing me on board again in 2022. It has been both fun and tremendously challenging - but never boring. So long and all the best @HaasF1Team."
Komatsu, 47, takes over having previously filled the role of trackside engineering director.
"In appointing Ayao Komatsu as team principal we fundamentally have engineering at the heart of our management," said Gene Haas.
"I'm looking forward to working with Ayao and fundamentally ensuring that we maximise our potential - this truly reflects my desire to compete properly in Formula 1."
Komatsu, who has also been with the team since its debut season in 2016 when he was chief race engineer, has over 20 years of experience in motorsport having also worked for British American Racing and Renault.
He takes over responsibility for the team's overall strategy and on-track performance, with a brief to maximise the team's potential.
"Having been with the team since its track debut back in 2016 I'm obviously passionately invested in its success in Formula 1," said Komatsu.
"I'm looking forward to leading our program and the various competitive operations internally to ensure we can build a structure that produces improved on-track performances."
The 2024 season starts with pre-season testing in Bahrain in late February followed by the opening grand prix at the same track on March 2nd.
