Heath, who is currently editor of Press Holdings' weekly business magazine The Business and associate editor of current affairs title The Spectator, will start his new role on March 3.
He joined The Business in 2002 and held roles as deputy editor and economics editor before being promoted to editor in January 2007.
David Hellier has been acting editor at City AM for the last six months, following Parsley's departure in August last year for family reasons.
Jens Torpe, chief executive and co-founder of City AM, said: "Allister reflects many of the qualities of City AM -- young, established in his field and ambitious.
"I've no doubt Allister will appeal to our readership, advertisers and the journalists on the paper.
"I'd also like to thank David Hellier, who for the last six months has been acting editor of the paper -- he has done a fine job in changing circumstances and we are immensely grateful for his support. We look forward to his ongoing contribution."
Hellier will be resuming his role as deputy editor of City AM.
Heath said: "[City AM's] editorial team is fantastic and the paper they produce so professionally every day has established itself as an essential read.
"I now intend to build on their hard work to take City AM to the next level and make it the best, most talked-about and most exciting paper for everybody who works in the city of London."
City AM launched in September 2005 and now has a daily circulation of just fewer than 100,000, according to the latest ABC figures.
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