He will take responsibility for the sale of sponsorship and TV promotions on behalf of channels within Box TV, its joint venture with Channel 4.
Box's seven channels include Kiss, Magic, The Box, Kerrang!, Smash Hits, Heat and 4Music. Luck will report to Bauer's head of broadcast sales, Karen Stacey.
Luck joined Bauer in 2007, after holding the position of group account director at SUB TV. At Bauer, he spent three years as a TV account director, and the last three as TV controller. He previously worked at Digital Media Sales and Universal Studios TV Network UK.
In a second promotion, Rachael Abraham has been appointed account director for TV.
Stacey said: "We continually look to improve customer service through the development and enhancement of our teams, and this promotion is a great example of that.
"We are confident that Martin's vast experience will lead to further success for the Bauer Media UK TV team, as it continues to offer innovative advertising solutions and gain access to new and existing audiences."
Last week, Bauer launched a streaming service for its seven TV channels. Magic, Kiss and Kerrang are now available on Freeview by pushing the red button from 4Music's channel 18 slot. All seven channels can be viewed through a streamed service on their individual websites.