There are several ways to answer your question. No exact answer can be given because there are variables not yet known which could dictate the amount of time needed to close after a purchase agreement has been negotiated, such as the type of mortgage (if any) you might be applying for, whether your credit and finances are in good enough order to complete a loan application; the seller's time frame needed to vacate; the timeliness of the required mortgage appraisal of the property, and of course the professional abilities of the mortgage loan officer and the underwriting team to process your file- and what type of inspections you plan to have and what type of repairs (if any) the seller will be required to complete prior to closing.
That said, you can close in as short as a week- or two months and anywhere in between. Planning and using able vendors in the transaction will make all the difference in the world.
I'm ready if you are!