The announcement has triggered a by-election in Aston, less than a year after he narrowly held on to the outer Melbourne seat at the 2022 poll.
Mr Tudge's resignation will be effective from next week.
In an emotional speech to parliament, Mr Tudge said his decision to resign was cemented following the death of his father earlier this year.
"It's not been an easy decision for me, but it is necessary for my health and for my family, amongst other reasons," he said on Thursday.
"I certainly have not taken this decision lightly."
Mr Tudge said his resignation was also due to him wanting to spend more time with his children.
"My daughters who are 18 and 16 know nothing other than their dad being away. They've had to put up with things that no teenager should have to including death threats, the most recent of which was last week," he said.
"My son is a bit younger, but I equally want to be a good father to him."
Mr Tudge, who has been in parliament since 2010, held the seat by 2.8 per cent after suffering a swing of more than seven per cent.
He previously held ministries in the education and human services portfolios under the previous coalition government.
Mr Tudge stepped down from cabinet after he was accused of emotional and physical abuse by his former staffer Rachelle Miller, with whom he admitted having an affair.
He has denied the claims of abuse, and opted not to return to cabinet once an investigation found Mr Tudge did not break cabinet rules.
Ms Miller was in parliament's public gallery when Mr Tudge announced his resignation.
The outgoing MP cited his work on the cashless debit card and work in education among his achievements in parliament.
"While this profession can be unforgiving at times, serving as a member of parliament, though, has been one of the greatest honours of my life," he said.
"I leave honoured to have served and proud of what we have achieved both for the people of Aston and across Australia but particularly for Indigenous Australia.
"It is time to pass the baton to someone who can hopefully serve our local community better than anyone before them."
Last week, Mr Tudge gave evidence at the royal commission into the robodebt scheme, where he denied he was responsible for checking whether the debt recovery program was lawful.
The by-election date has yet to be set.
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