Combined with a marksman-like kicking game, Laidlaw's most notable displays came in the club's historic Heineken Cup campaign, slotting nail-biting winners against London Irish and Racing Metro before controlling the club's famous Heineken Cup quarter-final win over Toulouse.
He said: "It's a huge honour to be Edinburgh Rugby captain. It's a role in which I take great pride and enjoyment. It's taken a lot of hard work to get to this point in my career but that level of commitment is no less than is required to excel at this level of the game and to achieve the success we all want for this club.
"Our squad is as strong as any I can remember, with players that were crucial to our successes last season signing up for more and some quality new signings joining to strengthen our league and cup campaign in the season ahead.
"It's very exciting, there's a lot of talent and potential driving us all forward and we're all looking forward to getting out there and building on the successes of last season."
Bradley said: "Greig was a stand-out player last season and, as captain, was crucial to the performances of so many key players and to the performance of the team as a whole.
"There are a number of key values that I want to see at Edinburgh Rugby and Greig is a classic example of how we want the club to operate.
"He is an excellent professional, is exceptionally committed, an inspirational leader and a consistent performer; there's little more you can ask of your captain.
"Under his leadership and the support of our two vice-captains, I believe this club can look forward to another landmark season."
Edinburgh are in Pool 1 of the Heineken Cup along with Munster Rugby, Saracens and Racing Metro 92.