Companies formed in Israel take several forms, any of which can potentially be done by a foreign entity (a person or corporation):
foreign company registered in Israel
limited liability company (LLC)
nonprofit
Israeli partnership
All of these require approval of the Israeli registrar of corporations and has different requirements.
Name
The company needs an original name, and three alternate names.
Shareholders
At least one shareholder is needed in order to establish an Israeli company. This entity may be an Israeli or foreign citizen, or another corporation.
An Israei citizen as shareholder will need to sign some documents (described below) with a lawyer as witness, while a foreign citizen is asked to attach a copy of their passport to the company registration application. A person (as opposed to corporation) wanting to register a company in Israel will need an Israeli ID or passport, home address, phone number, and an address for the company in Israel.
An international corporation shareholder will need to present an authenticated, translated certificate of registration. The owner of the company will either need to come to Israel and sign the documents in front of an Israeli lawyer and sign an affidavit declaring that there is no legal limitation for them to establish the company in Israel, or will need to sign the relevant documents in front of a consular official at the Israeli Embassy abroad or verified by an apostille, which may require translation of documents to the relevant language and will be more complicated than registration of a company while in Israel.
Fee
A registration fee is paid the Israeli government Department of Corporations at the Ministry of Justice. As of 2021, the fee for the registrar of companies is 2,645 NIS (~770 USD).