Mr Porter and The Outnet chiefs leave Net-a-Porter group
Tansley was formerly VP ecommerce at Net-a-Porter.com and stepped up to the role of managing director of menswear site Mr Porter in 2011. His role will be taken on by buying director Toby Bateman, according to Drapers.
Phair joined the group in 2009 to launch the off-price site The Outnet and went on to build a £100m business. She also sat on the group's executive team for seven years.
Her role will be split between vice president of global buying Shira Suveyke and global sales and marketing director Andres Sosa.
The news comes days after the newly merged group raised its annual cost-savings estimate from Euros 60m to Euros 85m.
Net-a-Porter's £2.8bn merger with Italian group Yoox was announced earlier this year and confirmed last month. Yoox chief executive Federico Marchetti was made CEO of the enlarged group, while Net-a-Porter founder Natalie Massenet, who was due to be its chairman, quit in September.
Massenet went on to set up Imaginary Ventures, an investment vehicle, and is understood to have taken a stake in designer Erdem's business.