The account has traditionally billed around £2 million but this is expected to jump to around £10 million when the company begins its makeover in November.
The switch reunites the account with Garry Lace, who ran it at TBWA before taking over as Grey's chief executive at the end of last year.
The account will be split between Grey and its Joshua subsidiary, which will take on all the Air Miles below-the-line activity.
Grey's task will be to establish Air Miles as a holiday company and make a rival to Nectar, the loyalty scheme run by Loyalty Management UK with partners including Sainsbury's, Debenhams, BP, Vodafone and Ford.
Lace said: "We've come up with something that isn't so much an advertising idea but more a brand repositioning."
He added: "It's a complicated task because the company has a number of target audiences including the people who have clocked up Air Miles but don't use them."
Drew Thompson, the Air Miles managing director, said: "Grey has changed over the past nine months and we're looking to build a long-term relationship with a group of like-minded people."
The move ends TBWA's three-year tenure of the Air Miles account. The agency's chief executive, Andrew McGuinness, said: "Drew has seen something at Grey that he feels is more in line with his personal vision for the Air Miles business."