Geldof and Yates were married for almost ten years before their divorce in 1995, and had three children together.
"When she left me I was destroyed," Geldof revealed, during an interview with BBC Four. "I didn't understand why, [I] never saw it coming."
The former Boomtown Rats frontman admitted that his depression got so bad that at one point he actually wrote out a list of pros and cons to help him decide whether to continue living.
"There was only one item in the list for why I should continue," he continued. "It just said, 'The children'."
Geldof previously said that he still feels haunted by Yates's tragic death in 2000 from an accidental heroin overdose.
"It was so mad and ultimately epic in its tragedy, Shakespearean," Geldof said, when asked how he felt about Yates's death. "I don't think you can describe it any other way."
The musician recently hosted a one-off charity concert in Sydney to help raise money for the victims of recent natural disasters.
Bob Geldof's revealing interview on Meeting Myself Coming Back will air on BBC Four on July 2.