Official patches for Magento 1.x PHP 7.2 compatibility are now available.

This applies both to Enterprise and community versions of Magento 1.x.

Starting from Magento Commerce 1.14.4.0 and Magento Open Source 1.9.4.0 PHP 7.2 support will be included in the core.

Resources:
– Magento 1.x PHP 7.2 Patches
– PHP 7.2 Patch install instruction