Mandi Taylor, also a managing partner, becomes deputy managing director. The third managing partner Patrick Norrie, who joined from Rapp's London office in 2007, is leaving Rapp to return to London.
Norrie said: "I'm heartbroken at leaving RAPP -- it's been a huge part of my life. But ultimately I had to make a decision that was right for me and my family."
Heaney rejoined Rapp in August 2007 having previously worked there for seven years from 1996 as head of client services.
Marco Scognamiglio, Rapp Group CEO and a former MD of the Edinburgh agency, said: "Discussions with the key partners led to a consensus that we needed real clarity in leadership if the business was to meet the challenges ahead and take full advantage of the opportunities it gets.
"Rebecca has outstanding leadership qualities and I'm convinced she will take the agency on to even greater heights."
Rapp recently gained a place on the Scottish government's DM roster as well as winning a marketing account from Co-op Financial Services and the Scottish Development International DM brief.