Yes, it is generally possible to execute documents electronically because no statutory law or regulation prohibits adopting a digital signature or using an e-signature platform when executing documents in Japan. However, note that the evidential value thereof may still be an issue. 

This has been addressed under the Act on Electronic Signatures and Certification Business (Denshi Shomei oyobi Ninshou Gyoumu ni kansuru Houritsu, Act No. 102 of 2000 ("E-Signature Act")). The electronic signature will be recognized under the E-Signature Act as constituting prima facie evidence of the execution of the relevant document when an electronic signature on electronic documents satisfies the following requirements:

• It is technically designed to indicate that the electronically signed contract has been created by the person who affixed the e-signature. 
• It is technically designed to detect any alteration that is made to the electronically signed contract.
• It is affixed by a party to the contract by using a unique code and device that is possessed exclusively by that party.

In forms of registry at the Legal Affairs Bureau for the purpose of perfection of mortgage or other security over real estate, for example, it is possible to register/perfect security electronically. However, the relevant e-signature must be made with one of the e-signature platforms provided by one of the few  service providers listed as permissible by the Ministry of Justice of Japan. Where the relevant parties cannot use the listed e-signature platforms, wet ink signatures will still be required. Furthermore, where an application to register a mortgage is submitted by a judicial scrivener, wet ink signatures will be required for some of the application documents.