Most Helpful Guy
It is a good idea to apologize for your wrongs. Then just tell him that if he ever changes his mind about you, that you will welcome him back into your life. Then walk away.
If he wants you in his life, he will call you. If he does not want you back in his life. . . then you don't want him because you will make him miserable and that will not work.
Most Helpful Girl
So, not so dissimilar from you i broke up with my now fiancé. In a bad moment, I over reacted and broke up. Regretted it later, at first he would have nothing to do with me. I sent him a note and apologized and asked him to contact me. He eventually did and we worked through things and did get back together a couple months after we started talking again. Now engaged. Most everyone told me to walk away and leave it alone, but I stuck with it and I'm super glad I did. Maybe the best choice I ever made. It took a fair amount of work to set things right and we had to work through some stuff, but I'm really happy about things now.