The former Liberal MP Sarah Henderson will return to federal parliament after winning preselection to fill a Victorian Senate vacancy.

Henderson defeated Greg Mirabella, the husband of former Liberal MP Sophie Mirabella, in the contest on Sunday.

The prime minister, Scott Morrison, federal MPs and other Liberal heavyweights including the former party president Michael Kroger threw their support behind Henderson, who narrowly lost her seat of Corangamite at the federal election in May.

She will replace retired senator Mitch Fifield, who resigned from parliament after the election to become Australia’s ambassador to the United Nations in New York.

“My intention is to hit the ground running, to work incredibly hard for the Liberal party, for the members who have selected me today and for the people of Victoria,” Henderson told reporters.

“I will be working around the clock, right across this great state, representing the people of Victoria. I am incredibly proud and honoured to be selected today.”

The neck-and-neck race between Henderson and Mirabella was at times marred by factional feuding.