It follows what he calls a 'moral failure' concerning his marriage.
His wife, God TV cofounder and director of television, Wendy Alec, will continue to lead the network along with its senior management team and the support of the God TV Board.
In a statement to God TV staff, Mr Alec said: "After 20 years of service, I have had a moral failure this year.
"For this reason, I am stepping down.
"Please forgive me for the disappointment I've caused, but I know your eyes are on Jesus who is the author and finisher of your faith and not on me, an imperfect man."
Wendy Alec will address viewers to update them on the situation next week from God TV's Jerusalem studio, where she will host a series of live Revival Alert broadcasts.
"I will take responsibility on the first night of Revival Alert to share with transparency and authenticity regarding the situation to all our viewers and partners," she said.
God TV began broadcasting on 1st October 1995.
It says it can now reach a potential viewership of 951 million people in 200 nations and territories.
Last year, Manchester United footballer Wayne Rooney said he enjoyed watching the channel.
