You need to clearly tell him what he needs to succeed in the job, and lay out what might happen if he does not. Providing you have the authority to put him on a PIP (Performance Improvement Plan), you might need start there, or at least plan on going there quickly.
Bob, I need some changes in your work. When you promise that something will be done today, it needs to either be done today, or you need to come to me very quickly and let me know what your roadblocks are. And I need you to accomplish task X in 1 hour or less, not 4 hours. I am concerned about your performance, and I would like to see some improvement quickly. Do you think you can do that?
Be willing to offer additional training, if he asks (and that is appropriate), and be willing to remove roadblocks. But don't be willing to do his work just because he won't.
Alison at AskAManager has good advice about using direct language at this article: Sugarcoating feedback. There is also a lot of information about when to issue a PIP.
It sounds like you've already tried the clear language, so it's time to move to the PIP. But since you're new, you need to do it properly. Therefore, you need to talk to your boss. Lay out what you've done, and what you think you need to do now. And ask for the proper procedures to follow company policy.
Boss, I have been very clear with Bob on what he needs to do, and he still is failing to even meet the basic expectations for the job. I would like to put him on a PIP, and if he doesn't improve quickly, have him moved out and replaced with someone who can handle the job. What are the policies for PIPs here, and can you guide me in this process?