First of all you may have your customized Exception Handler class, it will replace the default 
ResponseEntityExceptionHandler
Below is one sample code I used during my studies:
@ControllerAdvice
@RestController
public class CustomizedResponseEntityExceptionHandler extends ResponseEntityExceptionHandler {
    @ExceptionHandler(Exception.class)
    public final ResponseEntity<Object> handleAllExceptions(Exception ex, WebRequest request) {
        ExceptionResponse exceptionResponse = new ExceptionResponse(new Date(), ex.getMessage(), request.getDescription(false));
        return new ResponseEntity<>(exceptionResponse, HttpStatus.INTERNAL_SERVER_ERROR);
    }
    @ExceptionHandler(UserNotFoundException.class)
    public final ResponseEntity<Object> handleUserNotFoundException(Exception ex, WebRequest request) {
        ExceptionResponse exceptionResponse = new ExceptionResponse(new Date(), ex.getMessage(), request.getDescription(false));
        return new ResponseEntity<>(exceptionResponse, HttpStatus.NOT_FOUND);
    }
    @Override
    protected ResponseEntity<Object> handleMethodArgumentNotValid(MethodArgumentNotValidException ex,               HttpHeaders headers, HttpStatus status, WebRequest request) {
        ExceptionResponse exceptionResponse = new ExceptionResponse(new Date(), "Validation Failed", ex.getBindingResult().toString());
        return new ResponseEntity<>(exceptionResponse, HttpStatus.BAD_REQUEST);
    }
}
You can then add your customized Exceptions and complement the response object if you need it.
Please find the complete code with the other classes over here