Birmingham midfielder Charlee Adams has signed a new one-year contract with the club.
Southampton are confident Jay Rodriguez will commit to a new long-term deal but the player will consider his options.
The 20-year-old shot to prominence at the under-19 AFC championship, scoring all six of Australia's goals at the tournament to help them qualify for the 2013 FIFA under-20 World Cup.
He has never played a senior match for Fulham, but made eight appearances for Dutch club FC Eindhoven on a recent loan spell.
"It is important to establish relationships with clubs around the world and it is exciting that we are now forming one with an English Premier League side," Phoenix coach Ricki Herbert said.
"Having players coming this way is good for the future of the club."
Gameiro should be available to make his debut next week against the Brisbane Roar.