* He did as he promised. This is the most likely completion, assuming the previous context is about a promise made.
* He did as he had promised. This option clarifies that the action was done in accordance with a past promise.
* He did as he would promise. This option implies that he acted as he would typically act when making a promise.
You need more information to determine the most appropriate form of the verb. What was the promise about? What is the overall context of the sentence?