The board is appointed by the federal government, with Milne, who is also chairman of MYOB and a former NBNCo director, chosen for the role by his friend and former PM Malcolm Turnbull previous year.
News of Guthrie's departure was reported by The Australian before the decision had been communicated to ABC staff.
- 'I've got to say, I'm perplexed. She was smart and we were excited.
"The government thanks Michelle Guthrie and acknowledges her service as managing director of the ABC for the past two and a half years in what is a challenging and rapidly changing media environment.
In the first two years of my five year term, I have invested more in investigative journalism, more in regional journalism, more in innovative content and increased the efficiency and effectiveness of the ABC", she said.
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Senior journalist Sally Neighbour, executive producer of 4 Corners, tweeted: "Excellent decision".
She was also critical of the government's competitive neutrality inquiry into how the ABC and the SBS operate alongside their commercial counterparts.
"I believe there is no justification for the board to trigger that termination clause. This is entirely a board decision".
Mr Milne conceded Ms Guthrie had done a "pretty good" job turning the ABC towards its digital future.
Anderson will serve as acting managing director while Guthrie's permanent replacement is found. Anderson is now Director, Entertainment & Specialist and has worked in the media industry for more than 30 years.
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In an email to staff on Monday afternoon, Mr Anderson said he was honoured at the appointment.
"I wanted to continue the transformation of the ABC and to support the great work of ABC's dedicated and passionate employees to ensure our continuing trust, quality and distinctiveness as the source of Australian culture, conversations and stories".
Faine, who hosts the morning program on ABC radio in Melbourne, said Ms Guthrie "wouldn't advocate for us, which is an astonishing fail".
"This includes refocusing daily journalism away from lifestyle content and "clickbait" and back towards news and current affairs", the union said.
ABC managing director Michelle Guthrie has been sacked effective immediately because it was "not in the best interests" of the broadcaster for her to stay in the job.
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Deputy Labor leader Tanya Plibersek said she was perplexed by the decision and the board's statements had not clarified it.