It depends.  How much time was indicated on the contract?  A question to consider.  Is the Seller buying another home they need to move into and if so,  where are they exactly in their transaction?  Usually it takes about 30 days to close a 'smooth' transaction on a purchase.  If the Sellers transaction turns out to be a nightmare than they can cause grief on your end.  Not good.

Enter Occupancy Agreement.  In most cases Buyers give Sellers a week to move out.  If the Sellers need more time to move out you can have your Real Estate Agent execute an Occupancy Agreement so they pay you rent on a per diem bases (daily). 

Work with each.  Be understanding each others needs. 

In addition to the above answers, most conventional and FHA loans REQUIRE the buyer to take posession within 30 days. One notable exception being an FHA 203-K which is a rehab loan and the buyer has up to 6 months to rehab the home before taking posession. This is done as protection for the lender to avert some investment property loans from being portrayed as owner occupied loans.

Check with the lender and see what kind of mortgage it is and what the occupancy requirements are. Having a "side agreement" with the seller doesn't override the lenders requirements. It's possible the lender could call the note "due" or flip it to an investment loan if you don't take posession. Probably won't...but it's possible.