The hedge fund Starboard Value on Tuesday won consent from 54 percent of Darden shareholders to call a special meeting, sources familiar with the issue told CNBC. That gives the restaurant company a 60-day deadline to call the meeting and consider a nonbinding shareholder proposal.

Darden shares rallied after the news. Starboard is run by activist investor Jeffrey Smith, who has been waging a public campaign to keep Darden from spinning off its Red Lobster restaurants into a stand-alone company.