What he needs to know first is that you won't treat him badly ever again.
It is that simple!
So, you need to go to him and apologize.
Tell him exactly why what you did was wrong.
And... Tell him exactly why it won't happen again and what you would do if you were faced with the same type of challenge again in the future.
Can you do that?
Will you get him back?
Well, if he has already another woman in his life, your chances are slim.
But he certainly won't give you even the slightest chance if he believes he will be treated badly by you in the future.
So, invite him for a drink and tell him in detail why it won't happen again.
By the way, a vague "I have changed" is not enough.
You need to understand in great detail why your behavior was wrong and what is different now.