The company said Collie, who announced recently that he was to leave BAA at the end of this year "to pursue other interests", had made the change to devote more time to his new role as non-executive chairman of Lastminute. He joined the company as a non-executive director in 2000.
Leighton, who coined the phrase "going plural" when he left grocer Asda to take on a number of different directorships at a range of companies, said he would leave Lastminute at the beginning of next year, adding that he was also to resign his non-executive position at fitness chain Cannons and a directorship at Dyson.
However, he will continue as chairman of the Royal Mail and Bhs, as well as retain his position on the board of BSkyB.
Brent Hoberman, CEO and co-founder of Lastminute, said: "Allan has done an excellent job for us, leading the board through an exciting and challenging growth period and we are sorry to see him go. However, we are delighted that Brian is in place and ready to take over next year. He has been with Lastminute almost since inception and is held in high regard by both the board and the executive team.
"His experience at BAA, combined with his knowledge of the retail, travel and tourism markets, will be invaluable as we roll out the next phase of the Lastminute strategy."
Lastminute shares dipped on the news, dropping 1.2% to 103.75p by mid-morning.
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