The musicians had been quietly dating since meeting during a recording session for her new studio album in February of this year, reports People.
"A romantic relationship blossomed as they spent time writing together," a friend of Lavigne is quoted as saying.
Kroeger proposed with a 14-carat diamond engagement ring on August 8, and a second insider added that the couple's families "could not be more excited" by the news.
This will be Kroeger's first marriage. Lavigne was previously married to Sum 41 frontman Deryck Whibley between 2006 and 2009.
She broke up with Brody Jenner at the start of 2012, following a two-year relationship.
Lavigne also confirmed earlier today that her new album is complete and said that she is "super-stoked" about its release.
Watch the music video for 'Girlfriend' by Avril Lavigne below: