Insiders claim Smith made it clear that he wanted to leave after his role was reduced following a restructure in June.
Smith went from overseeing all the energy supplier's marketing to strategy alone when it split its operation into two divisions.
Mackenzie quit her role as Hewlett-Packard's vice president of marketing, EMEA, last month. She joins British Gas as director of brand marketing on November 1 and will report to division managing director Mark Clare.
Smith oversaw the launch of its "Doing the right thing" activity, moving its £26m ad account to Clemmow Hornby Inge from DDB London. He is currently chairman of The Marketing Society.
Clare said Mackenzie's "experience in consumer markets and household-name brands means she is very well placed to build on what Nick has achieved".
Separately, British Gas head of marketing Charlie Herbert has resigned from the company. He is joining home emergency-services provider Homeserve as marketing director.
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