Cr Conroy, the mayor of Frankston City Council, was announced on Sunday as the party's choice to contest the seat at the upcoming by-election.
"I will always listen and I will work hard to ensure this community remains a wonderful place to live, work, raise a family and retire," he said.
"I love this community. It's a privilege to serve as mayor of Frankston City.
"But there is so much more to be done to deliver for this community and that's why I've put myself forward for Dunkley."
The by-election has been triggered by the death of the Labor MP, who died in December after a long battle with cancer.
Cr Conroy said he wished his candidacy wasn't in "such sad circumstances," while paying homage to Ms Murphy as "both fearless and tireless in advocating for her community".
Victorian Liberal Party President Philip Davis said Cr Conroy will be a "strong voice" for local families struggling with rising living costs.
"This is an opportunity to send a message to a government that has been focusing on the wrong priorities and must do better to tackle rising costs felt throughout our community," he said.
"Labor has short-changed Victoria and recently cut funding for local infrastructure, breaking its promise to fund the Frankston Baxter Rail Upgrade.
"Nathan Conroy will work tirelessly to ensure Dunkley is place where young families can build a great future."
A date is yet to be set for the poll in the seat on Victoria's Mornington Peninsula.
Labor named Frankston community leader Jodie Belyea as its candidate last week.
Ms Murphy held the Victorian seat from 2019 and increased her margin at the 2022 federal election.
The most recent poll showed Labor recording a three per cent swing to hold the marginal seat by 6.2 per cent.
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