The 26-year-old led England to a second-place finish in last year's campaign, but was not confirmed as skipper when the initial squad was named on January 9 amid concerns over his decision-making.
Head coach Lancaster has now officially named the Harlequins flanker as his captain ahead of the tournament opener against Scotland on February 2.
Lancaster said: "Chris stepped into the role 12 months ago, when we were building a new team, and he has grown as a leader on and off the field.
"He showed those leadership qualities during the QBE Internationals, and especially against the All Blacks when the whole squad got behind him.
"We have a number of leaders and I know they will all take this team forwards with Chris as we look to kick on from that result."
Robshaw has won 12 England caps since debuting in 2009.