Blatter announced earlier this month he was standing down after the body was hit by a wave of corruption allegations that are still sending shockwaves around the footballing world.
The 48-year-old Bility is the second person to declare his candidacy after former Brazil international Zico.
"We all agree in the world that football is facing a difficult moment and it is in difficult moments that great leaders emerge," Bility told BBC Sport.
"Africa is the largest voting bloc in FIFA and we must take the lead to bring football together."
Bility, who has led the Liberian FA since 2010, is not afraid to make a stand as in 2011 he broke ranks with the majority of his African colleagues by stating he would vote against Blatter.
In 2013, the Confederation of African Football (CAF) banned Bility for six months for violating statutes relating to the use of confidential documents.
Bility confirmed he had yet to receive the backing of five soccer associations, as required to stand in the race, but was confident of securing the support of his continent.
"People know me to be bold, upright, outspoken and highly opinionated," said Bility.
"I say it like it is. When it's not right, I don't back down and I think that has gained me some respect.
"I have spoken to about half a dozen of the presidents of African football and I have their support - you can see the excitement.
"If I have one reason to believe that Africa is not going to stand by me, I am not going to put up my candidacy."
The date for the presidential elections is expected to be announced after FIFA holds an extraordinary meeting of its Executive Committee in July.
(Reporting by Pritha Sarkar, editing by Toby Davis)
