The 25-year-old led England to away wins over Scotland and Italy, and the Harlequins flanker will skipper the side against Wales at Twickenham in their next clash on 25 February.
“Chris has stepped into the role well and led a new team in two tough away fixtures,” said Lancaster.
“He is one of many leaders we could have chosen against Scotland and Italy but he has shown on and off the field the qualities required to captain a side.
“We feel it is right to make a call now that Chris will lead England for the rest of the Six Nations.”
Robshaw, capped three times by England, could not hide his delight at being handed the role and is looking forward to leading his side out at Twickenham.
“Captaining the team against Scotland was the proudest day of my life and to get the chance again against Italy was fantastic,” said Robshaw.
“To do so at Twickenham would be something else and I’m thankful to the coaches for giving me that opportunity and to all the lads for helping me over the last few weeks.
“For now I’m just focusing on training hard and helping us get ready to play a strong Welsh team.”
Meanwhile, 15 England players will be available for selection in the Aviva Premiership this weekend when they leave the national side’s camp on Wednesday night, while Ben Morgan and Tom Palmer will be free to play for their respective sides Leinster and Stade Francais.
“It’s important that we support the clubs and also that players get some game time so we can see where they are really up to in terms of fitness and form before we head into a Test week against an on-song Wales,” added Lancaster.
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