Rich will replace Mark Cranmer, the former global executive director at Dentsu Aegis Group, and will take up the chairmanship on 1 January.
Cranmer was made Magnetic's first chairman when it launched in March 2015 but is now stepping down to focus on other business ventures.
Emphasising his desire to take on a more active role as chairman than as founding partner, Rich said Magnetic has "only just begun" the job of proving how unique and engaging magazine environments are for advertisers.
Magnetic’s chief executive, Sue Todd, said: "Mark’s knowledge and experience has been invaluable in setting Magnetic's foundations over our first two years. He has been instrumental in driving more collective action from the sector and I have enjoyed working with him immensely.
"Marcus is of course already close to Magnetic and I look forward to having greater input and his ongoing support for big initiatives to help prove the contribution of magazine media."