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.
Head of the A-League Greg O'Rourke said there will be byes during the A-League next season.
"We’ll have the usual five games a round but with one team having a bye. One of our goals is to go to 14 teams so we have an even round. We could go up to 30 rounds if we needed to," O'Rourke said.
Meanwhile, Nikou confirmed future expansion plans and said it is just the start of the journey for the A-League.
“Our work on expanding the A-League does not stop here. This is the start of a journey which will see our competition grow beyond 12 teams in the future," Nikou added.
Western Melbourne and Macarthur are the first to join the league since Western Sydney Wanderers in 2012-13.
The bids beat four others, which were shortlisted in October, including long-term favourities Team 11, Southern Expansion, South Melbourne and Canberra.
Professional Footballers Australia chief executive John Didulica welcomed the FFA's move.
“The PFA welcomes the FFA Board’s decision to expand the A-League and we congratulate the successful communities and ownership groups who now inherit the responsibility of managing a football club in the A-League and beyond," Didulica said.
“The task ahead to ensure a competitive club is significant. It remains incumbent on the entire football community to provide the support that will be needed to help the new teams and the expanded competitions to succeed."