As part of the deal, Zendesk shareholders received $77.50 per share in cash.
Proxy advisory firm Institutional Shareholder Services (ISS) had backed the deal, which Zendesk shareholders approved in September.
Jana had pushed for the sale after San Francisco-based Zendesk failed to buy SurveyMonkey parent Momentive Global Inc in a $3.9 billion deal. The Momentive deal fell through after it was rejected by Zendesk shareholders.
In August, Light Street Capital Management, which manages funds that own more than 2% of Zendesk, said it would vote against the private equity deal and proposed that Zendesk remain a standalone public company and find a new top boss.
(Reporting by Akash Sriram in Bengaluru; Editing by Shinjini Ganguli)