I wouldn't recommend doing it, instead it's better to completely rewrite old application in Yii2.
But in case of partial migrating, please read this paragraph in Special Topics Section in Official Guide.
Here are some important code snippets from there:
1) Modification of entry script:
// include the customized Yii class described below
require(__DIR__ . '/../components/Yii.php');
// configuration for Yii 2 application
$yii2Config = require(__DIR__ . '/../config/yii2/web.php');
new yii\web\Application($yii2Config); // Do NOT call run()
// configuration for Yii 1 application
$yii1Config = require(__DIR__ . '/../config/yii1/main.php');
Yii::createWebApplication($yii1Config)->run();
2) Combination of Yii
classes:
$yii2path = '/path/to/yii2';
require($yii2path . '/BaseYii.php'); // Yii 2.x
$yii1path = '/path/to/yii1';
require($yii1path . '/YiiBase.php'); // Yii 1.x
class Yii extends \yii\BaseYii
{
// copy-paste the code from YiiBase (1.x) here
}
Yii::$classMap = include($yii2path . '/classes.php');
// register Yii 2 autoloader via Yii 1
Yii::registerAutoloader(['Yii', 'autoload']);
// create the dependency injection container
Yii::$container = new yii\di\Container;
Usage of Yii
class:
echo get_class(Yii::app()); // outputs 'CWebApplication'
echo get_class(Yii::$app); // outputs 'yii\web\Application'