Johnson made the comments in 2012 while appearing on a BBC1 series called 'The Big Questions' during which he opted not to back the an FA anti-homophobia campaign.
In a statement released by the FA on Thursday night, Johnson admitted he held "deep regret" over his comments on the television programme, adding that they were beliefs he no longer held.
The 40-year-old was named in a 10-man IAB panel last month, which has been designed to promote equality in the game.
The panel, which is due to meet later this month, is chaired by FA board member Heather Rabbatts.
Rabbatts has since spoken with Johnson and believes he has "a huge amount to offer to the Inclusion Advisory Board".
A report on the Guardian on Thursday night first flagged the footage from 2012, in which Johnson was asked by presenter Nicky Campbell if he would support the fight against homophobia.
Johnson replied: "Because of my beliefs, because of the Bible that I read, in the Bible it does state that homosexuality is detestable unto the Lord."
Johnson, who is an ambassador for Birmingham children's hospital, said in a statement that his views had since changed.
"I was invited on to the programme in March 2012 to talk about my faith," he said.
"I was not prepared for the question and it is with deep regret that I answered it in the way I did back then. It was wrong and relates to a view I no longer hold.
"I have since invested a great deal of my time and energies into re-educating myself through reading, attending workshops and entering into debates. As a result, my whole way of thinking has changed.
"The Inclusion Advisory Board is all about education and changing opinions and, through my own personal experience and learning, I believe I can have a positive influence on the work being done by football on this vital agenda."
Rabbatts added: "I have spoken to Michael in detail about this and I accept his account of what happened and his regret over the incident.
"More importantly for me and for Michael, we acknowledge that through his own personal journey he has a huge amount to offer to the Inclusion Advisory Board."
Human rights campaigner Peter Tatchell thinks the FA will still have to explain Johnson's appointment.
He said: "If Michael's change of heart is genuine, then I'm reassured. But why did it take criticism and pressure to get him to make a pro-gay equality statement? It came rather late in the day.
"The FA still has questions to answer. Why didn't they research Johnson's views on tackling homophobia before he was appointed? What were their criteria and procedures for making appointments to the equality board?
"The FA would never appoint a person who refused to support the campaign against racism. Why the double standards?"