edd_complete_purchase

This action runs when a payment is marked as complete.

Since EDD v1.6

do_action( 'edd_complete_purchase', $payment_id ); 

Simple example

function pw_edd_on_complete_purchase( $payment_id ) {

	// Basic payment meta
	$payment_meta = edd_get_payment_meta( $payment_id );

	// Cart details
	$cart_items = edd_get_payment_meta_cart_details( $payment_id );

	// do something with payment data here
}
add_action( 'edd_complete_purchase', 'pw_edd_on_complete_purchase' );