The American musician published a message on social media which read: "Several years ago I failed and sinned in my marriage".
Houghton, who was born in southern California, said he and Meleasa had been "working through this" for more than five years, however, he added "the challenges in our relationship have proven too much to overcome".
- Lives in Texas
- Worship leader at Lakewood Church, Houston
- Winner of five Grammy Awards
- Albums include 'Jesus at the Centre: Live' (2012)
In a post on his official Facebook page, the Grammy-winning artist apologised to anyone "hurt to learn of my personal failure".
Speaking of his relationship with Meleasa, he said: "We have always handled our family and ministry with grace and generosity toward others, discretion, and privacy.
"So, for the sake of our amazing kids, we are also handling this privately with pastoral oversight and assistance.
"We choose to remain friendly and kind to each other going forward. I am in the process of restoration and I have repented for my actions."
Houghton is known for songs such as 'Friend of God' and 'Again I Say Rejoice' which are sung at churches and conferences around the world.
When he's not touring with his band New Breed he is a worship leader at Joel Osteen's Lakewood Church in Houston, Texas.