The match will take place at The Den, home of Championship side Millwall, and serve as preparation for the World Cup finals, where Australia will take on Spain, the Netherlands and Chile.
Ecuador, captained by Manchester United's Antonio Valencia, have also qualified for the tournament in Brazil, drawn in a group with France, Honduras and Switzerland.
"We're excited to have secured the match against Ecuador, which offers us a good test against South American opposition leading into the World Cup," Socceroos coach Ange Postecoglou said in a statement.
"We have tried to secure opponents for the games leading into the World Cup to replicate the type of football we are expecting to face in Brazil and playing Ecuador gives us some quality South American opposition ahead of the first group stage match against Chile.
"This is also the last match we will play before we get together in May for our final World Cup preparations so it's important that we can build on the first positive steps we took in the match against Costa Rica late last year."
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