Gallop said the Socceroos had proved their worth by reaching the 2015 AFC Asian Cup final on home soil.
Saturday's clash with Korea Republic in Sydney will be the side's second successive title decider, having played eventual victor Japan in the 2011 edition.
"It was a really smart move by Frank Lowy and the FFA to move out of Oceania and into the Asian Football Confederation (in 2006)," Gallop told Sky Sports Radio.
"We are newcomers and it's great for us to have success at whatever level we're playing in Asia.
"But this is the big one, and to make the final, we'll cement our place in Asian football."
The FFA boss said he was very proud of the team's performances and reserved special praise for coach Ange Postecoglou.
"He knows what he's doing," Gallop said.
"We gave Ange the job 12 months ago to regenerate the team on and off the field. He had mixed results along the way as he tried out lots of players.
"But we've made big changes off the pitch as well - our sports science has had an overhaul; we've got Craig Duncan who's done work with the NSW State of Origin team involved and the boys are fit and raring to go for Saturday night and we're really proud of them."
Gallop said the overall success of the tournament had "exceeded expectations".
"I think we always knew that the Socceroos games would be well supported, but we've been pleasantly surprised at the way people have got out and supported the other games," he said.