Lindsay is leaving his current role as managing director, commercial, of in-flight media specialist Brand Connections Global but is understood to be working out his notice and is expected to join Amscreen in three months.
Lindsay, who has more than 15 years experience in the industry, will manage Amscreen's UK division.
Before joining Brand Connections Global in 2010, Lindsay led a 60-strong sales force at JC Decaux. He started his career at Carat, the Aegis media agency.
He will be joined by Jai Pushkin, who has been promoted to the role of head of agency sales.
The appointments follow on from other recent additions to the team including Yoko De Souza as director of client sales, Mike Hemmings as marketing director and most recently, James Whitbread as account director.
Simon Sugar, chief executive officer of Amscreen, said both Jamie and Jai had "fantastic industry experience" and the Amscreen team is "continuing to develop at a fast rate".
Amscreen operates and sells ads on a networks of screens located in forecourt stores, local convenience stores, WHSmith Travel stores, GP surgeries and Powerleague football centres.
Follow Nick Batten on Twitter @NickBatten2