Robshaw will lead his country for the first time when he wins just his second cap against the Scots at Murrayfield on Saturday.
The 25-year-old has beaten the likes of Dylan Hartley, Tom Croft and Ben Youngs to the role, although it is unclear whether he will remain in charge when Tom Wood returns from injury.
Northampton back rower Wood is currently sidelined with a toe injury but is expected to be back in time for the home tie with Wales on February 25.
"It's a huge honour and a very proud day," said Robshaw.
"It's not about myself, though, because there are six or seven guys around me who all have a massive role to play - there's lots of other leaders in the group."
Lancaster won't name his team for the Scotland game until Thursday but he insists Robshaw is the right man to guide England in the opening game of his tenure.
England's interim boss took his time choosing his skipper after admitting he wanted to see how the candidates performed at a training camp in Leeds but he is convinced he has made the right decision in opting for the man who has guided Quins to the top of the Aviva Premiership this season.
"We have a strong leadership group and I have been very impressed with the way they have all stepped up so far. Chris is a key member of that group and has shown with Harlequins and when I have worked with him in the Saxons that he can lead a team tactically and passionately," said Lancaster.
"I am delighted that he has got this chance at the highest level and I know it will be a very proud moment for him, his club, family and friends when he leads England out at Murrayfield on Saturday."