To "expiate" means to make up for, "God's tribunal" is the judging body of heaven, and "sanctions" means approves. In saying the words,
"It will expiate at God's tribunal. I know my maker sanctions what I do",
Mr. Rochester is telling himself that even though the world may say that what he is about to do in marrying Jane is wrong, he is sure that, in God's eyes, it is right.
Even though his first wife Blanche is a madwoman, Mr. Rochester is a married man. To become divorced in those times is out of the question, so if Mr. Rochester marries Jane, he will commit the crime of bigamy, having two wives. When he speaks the quote, Mr. Rochester has just gone ahead and proposed to Jane, and she has accepted with joy. He is now trying to justify his actions in his mind. He reasons that
"It will atone...have I not found her friendless, and cold, and comfortless? Will I not guard, and cherish, and solace her? Is there not love in my heart, and constancy in my resolves?"
Mr. Rochester figures that since Jane is needy, his intentions are good, and he loves her and will care for her, it will make up for the fact that he is going against God's law by marrying her while he is still married to Blanche. By following God's commands to love one another and care for the downtrodden, he is hoping that his transgression in committing adultery will be overlooked in the final analysis (Chapter 23).