The person who draws the cheque and sign on it is the drawer.
Explanation:
A drawer is the person who draws a cheque in the favour of his creditor. The cheque is signed by the drawer of the bill, who is the account holder of the bank. The drawer of the cheque draws the cheque on the bank, known as drawee, to pay the amount to the person in whose favour the cheque is drawn.
Payee is the person to whom the amount is payable.