The 29-year-old who joined from Watford back in October 2003 has signed a two-year deal, plus a further year's option in the club's favour.
"Robbo warrants his new deal," Tony Mowbray said.
"He was very consistent for us last year and has started this season well for for us.
"I'm delighted he's put pen to paper.
"Robbo is a good player and good players deal with whatever comes at them.
"If he's got to be physical, he's physical.
"If it's a football match, he's not found wanting either."
The fans' favourite started all but 3 of Albion's championship winning season last term and could not hold his delight at finally signing a new deal.
"I'm absolutely delighted," the left-back beamed.
"Obviously, these things take time.
"The manager and chairman wanted to get new players in first and I fully understand that.
"I'm glad it's all sorted now and I can get my head down and focus fully on my football again.
"I'm fully committed to the club - and I would have been whatever happened.
"The club have been good to me and there was never any doubt I wasn't going anywhere.
"Everyone's now got to put up with me for at least another two years!"