Current President Kang Young-joong of South Korea said earlier this month he would step down from the role in May after eight years spent increasing participation and developing the lucrative 'superseries' events.
Justian, who failed in a previous bid to head the organization in 2001, said he expected a challenge from Malaysian Badminton President Nadzmi Mohd Salleh.
The sport came under fire in London in July when four women's doubles pairs from South Korea, China and Indonesia deliberately played to lose their matches in order to get a more favorable draw. All four pairings were disqualified and banned after the farcical scenes.
The BWF also had to shelve plans to introduce a rule that all women players had to wear skirts in a bid to glamorize the sport after the move drew criticism from athletes.
Despite the problems, the London Games saw a record 51 countries participating in the sport, which strives to grow outside its main Asia base, with the BWF saying all sessions were sold out.
Justian said he wanted to build on that success and help the sport gain greater recognition from the International Olympic Committee (IOC).
"When it was first at the Olympics, badminton was ranked 26th (by the IOC). Currently it is between 16 and 17," he said.
"As candidates, we believe we have the experience, expertise and passion to propel badminton to even greater heights."