It was expected that Northampton back-rower Tom Wood would get the nod but his slower-than-expected return to full fitness has meant that Robshaw will lead England into battle against Wales, France and Ireland.
And despite winning just one cap before this year's Championship, Lancaster is adamant Robshaw has more than met his expectations after two wins from two.
"Certainly for the next three games we think it's the right decision," he said.
"It was an easy choice. He's respected, he leads by example and says the right thing at the right time.
"We were confident in his ability, even though he had one cap, to captain at international level.
"He did that well and backed it up with great performances, by topping the tackle and carry counts, in the first two games."
Robshaw is also captain at club level with Quins and admits he can't wait to lead his team out at Twickenham for the first time.
"I'm very honoured," he said. "It's great to have the backing of the players and the coaching team around me.
"Now it starts with going on to Wales and trying to improve our performance and get a win.
"I've been enjoying being captain. Of course, it would have been different if we had lost both our games. But there's a great feeling in the camp after two wins.
"Captaining the team against Scotland was the proudest day of my life and to get the chance again against Italy was fantastic.
"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 16 players have been released from the England camp to play for their clubs this weekend including Leicester pair Manu Tuilagi and Toby Flood, Northampton lock Courtney Lawes, and No.8 Ben Morgan.
Players released for club duty:
Mike Brown, Joe Marler, Jordan Turner-Hall (all Harlequins), Calum Clark, Paul Doran Jones, Courtney Lawes (all Northampton), Toby Flood, Manu Tuilagi, Thomas Waldrom (all Leicester), Lee Mears (Bath), Ben Morgan (Scarlets), Tom Palmer (Stade Francais), Charlie Sharples (Gloucester), Joe Simpson, Rob Webber (both Wasps), Matt Stevens (Saracens).