Blair missed out on selection for the original 37-man squad as head coach Ian McGeechan chose O'Leary, Harry Ellis and Mike Phillips as his No9s, but the 28-year-old says he never gave up hope of fulfilling his Lions dream.
"I'm really pleased to have been given the opportunity to tour with the Lions; it is a massive honour," said Blair, who becomes the third Scot in McGeechan's tour party.
"The call-up just goes to show how quickly everything can change in rugby and I'm determined to seize my chance and make an impact.
"Since the original squad was announced, I've just focused on playing well for Edinburgh and helping the team climb up the Magners League and fortunately that has helped me to get selected.
"I would like to thank the coaches at both Scotland and Edinburgh for helping me to achieve inclusion into the Lions squad and I'm excited about the challenge ahead."
Edinburgh head coach Andy Robinson echoed the sentiments of those within the Scotland set up as he praised Blair's attitude and commitment and congratulated his star player on his belated selection.
"It is an honour for Mike to be selected for the Lions and a reward for all the hard work he has put in over the past few seasons," explained Robinson, who coached the Lions alongside Graham Henry in 2001, having toured as a player in 1989.
"Mike has matured into an outstanding leader, for both Edinburgh and Scotland, and he is an intelligent player with a lot to offer the Lions selectors.
"I was fortunate enough to tour with the Lions, both as a player and as a coach, and it is the pinnacle of a player's career.
"I'm confident Mike's career will flourish as a result of the experience and he will come back to Edinburgh having benefited from the tour."