Agustien had been on trial with the Swans in the summer but the deal was put on hold following a knee injury.
But the 24-year-old has fully recovered and aims to make his league debut against Reading in the Championship next Saturday.
Swans boss Brendan Rodgers said: "Kemy has the attributes that can take him to the highest level in the British game.
"He is mobile, strong and a good player with the ball at his feet. He has everything we look for in a player."