Show him your commitment
While it is important for you to tell him that you have changed, it is the way you act that will show him whether you are truly worthy of his trust. While eroding his trust may have happened rather rapidly, you should not expect to regain his trust as fast. Be prepared to take time in the process of winning back his lost trust. However, if you are committed, your actions will gradually indicate that you are indeed worthy of his trust once more.
It starts with simple things. For instance, if you tell him that you are going somewhere, ensure that that is where you will be. Learn to return home straight after coming from work instead of hanging out with some friends. Let your friends visit you at home instead.
In general, you should develop a more transparent lifestyle that will not create some doubts in his mind. Let this be a permanent change, not just as an effort to regain his trust.
Trust him first
Many people find it difficult to share some parts of their lives with their partners even when they are in a stable relationship. However, if you would like to know how to regain his trust, you will need to begin by trusting him.
Be very frank with him as you bear out your soul. When he notices that you are sharing the deepest parts of your life with him, he will learn to trust you once more. Do not mind that you will start telling him about things you had previously held back. This is the best course of action. After all, you do not really want to bring things back to the state they were. Had that state been the best, you would not have cheated in the first place.
Be aware of the limits
As much as you may try to regain his trust after you have had an affair, it may never be possible to get a complete restoration. When he still seems to hold some part of himself back, understand that there are some things he finds difficult to forget so that he can trust you fully again.
What is important is for you to play your part fully. He also has a part to play in deciding whether he really wants to trust you again.