It depends on a variety of factors, including the type of mortgage you're looking for, your credit score, and the size of your down payment. But generally speaking, you can expect to hear back within a few days if you've submitted a complete application with all the necessary documentation.
Keep in mind that pre-approval is not a guarantee of final approval. Your lender will still need to do a full evaluation of your financial situation before issuing a final loan commitment. So it's important to stay disciplined and avoid making any large purchases or taking on new debt while your loan is under review.