Strahota announced her resignation as 3rd District alderwoman in July because she is moving out of the city.
Westby, of 507 E. Fulton St., was one of two candidates to apply for the job. The other was Luke Gersich, 202 E. Fulton St.
Westby, 53, served on the city council from 2007 to April 2009, when Mark Wellnitz defeated him by one vote.
A project engineer and information technology manager for Johnson Industries International, Westby now serves on the City Hall Design Committee.
Westby wants to continue serving Edgerton because he loves the community, he said.
Gersich, 31, is a network engineer by profession and is retraining to update his skills, he said.
He took classes in local government in college and wanted to bring fresh ideas to the city, he said.
Strahota was appointed in April 2008 and was elected in April 2009.
"Serving on the city council was such a great honor to me, and I adore and respect all those that I was able to interact with," she wrote in an e-mail to The Janesville Gazette.