The move finally fills the role left vacant when former chief executive Garry Cook was forced to resign in September last year. Cook quit after sending insensitive emails regarding the condition of cancer sufferer Dr Anthonia Onuoha, who had been acting as the agent of her son, then City defender Nedum Onuoha.
American Glick, who worked in minor league baseball and the NBA in his homeland before joining the Rams in 2008, is due to take up his new role in August.
City's interim chief executive John Macbeath said: "Since September 2008, Manchester City has been a club in constant development and evolution.
"With many milestones achieved in terms of on and off-field developments, it is important that we recognise that we must now further evolve in order that we can continue to create and capture potential opportunities for the club.
"To do that we need the very best people and the board believes that Tom is the ideal person for this role. We very much look forward to the contribution that he will make."
Glick said: "I am very pleased to have been offered this opportunity at Manchester City Football Club.
"This is an exciting time for all connected with City, and I am looking forward to joining and helping to drive the club's off-field development on its future journey.
"I have been impressed by the ambitions and plans set out by the chairman and board.
"I shall use my experiences here in England and in North America to help City build on its recent successes and achieve new milestones in Manchester and around the globe."