Vidic has in recent weeks been heavily linked with a move to Spanish giants Real Madrid.
Gill told MUTV: “I am very pleased to confirm that we agreed terms with Nemanja three or four weeks ago on a new long-term deal with the club.”
Gill continued: “We sat down with Nemanja and his advisor at the end of last season and started discussions. They broke up when Nemanja went away to the World Cup, but resumed when Serbia were knocked out.
“It’s yet to be signed – the paperwork is now being sorted by our lawyers and being checked by Nemanja’s advisors. He’s still away on holiday but the plan is that when he gets back the papers will be signed.
“We’ve shaken hands on it and we’re confident it will all be signed and sealed in early August. It’s great news for Manchester United and great news for Nemanja and the fans.”
He added: “There was a lot of speculation about Nemanja’s future, but in my view it’s been the media drumming some old stories.
“They certainly didn’t come out of the Manchester United camp and I’m confident they didn’t come out of Nemanja’s camp.”
