The non-binding deal values Vodafone Egypt at $4.4 billion and the two companies have agreed a arrangement over the long-term use of the Vodafone brand and other services in Egypt.
Selling the stake is in line with Vodafone's efforts to streamline its operations to focus on Europe and sub-Saharan Africa, Vodafone Chief Executive Nick Read said.
"It will reduce our net debt and unlock value for our shareholders," he said.
Vodafone said the transaction was expected to close by June. STC said the non-binding agreement was valid for 75 days from Wednesday and could be extended by mutual consent.
"Vodafone Egypt is the leading player in the Egyptian mobile market and we look forward to contributing further to its continuing success," said STC Chief Executive Nasser al-Nasser.
The binding agreement is subject to approvals by STC and Vodafone, and regulators. STC said no other parties were involved in the potential deal.
STC, also known as Saudi Telecom, is majority owned by Saudi Arabia's state fund the Public Investment Fund (PIF).
Telecom Egypt, which also owns a stake in Vodafone Egypt, said on Wednesday it was closely monitoring the process "to study all available alternatives for it to handle its investments in Vodafone Egypt".
The state-owned company said on Sunday it had no intention of selling its stake.