Both will report directly to Neil Duncan, head of client development, and Tim Forrest, head of communications planning.
Taheri, who has worked with a range of clients, including Diageo, Cadbury and Philips, will be the business director on OMD's Vodafone account.
At the same time, Glass joins as business director on the agency's PepsiCo and Hasbro accounts.
Glass was one of six senior figures at Carat who were appointed as group communication directors in 2006 when the Aegis agency restructured into six business units.
She has worked in media for more than 17 years, at Publicis Groupe agency Zenith, as well as Carat, across clients including Kraft, Asda, Arla Foods, Royal Mail and Nivea.
Duncan said the appointments would bring a "fresh approach" to OMD's handling of its Vodafone, PepsiCo and Hasbro accounts.