The Harlequins flanker has skippered England for all but two of Lancaster's matches in charge, but it was reported that Tom Wood had come under consideration for the role.
However, following the weekend's club fixtures, Lancaster has opted to stick with 27-year-old Robshaw.
"I've always said that prerequisite for a captain is to be selected on form and fitness," Lancaster told reporters. "Chris has shown during the first half of the season that he has been in great form.
"His experience as captain with us and Harlequins meant that it was a pretty easy decision. I'm sure he'll do a great job for us."
Meanwhile, Robshaw added: "Every time you pull on that white shirt it's a privilege. It's a huge honour to be named captain and to lead your country."
The three matches will see England take on Australia, Argentina and New Zealand next month.