As widely reported earlier on Thursday morning (AEDT), the Melbourne-based outfit will enter the competition in 2019-20 while the Sydney side is set to join a season later.
The FFA announced the decision during a press conference, after mass delays and speculation regarding A-League expansion.
"We have seen unprecedented interest from bids to be part of the A-League and we are excited about our two new expansion clubs in Sydney and Melbourne," FFA chairman Chris Nikou said in a statement.
"An expanded A-League will connect new communities in our two biggest markets, create new rivalries, bigger television audiences, more derbies and importantly, further opportunities for Australian footballers to play at the highest level in this country."
Western Melbourne will play their home matches at Geelong's Kardinia Park next season, until they fulfil their promise of building the first privately owned football stadium and training centre in Australia - with the FFA expecting it to be ready in 2022.
