Vlemmiks was promoted from the role of marketing director to commercial director in June 2010 amid a wider restructure of the senior management team, which was designed to give greater influence to brand marketing across the organisation.
Vlemmiks replaced incumbent Chris Jansen, who was promoted to the new role of managing director for British Gas Services in order to pull together the firm's consumer-facing elements.
Vlemmiks is now to leave at the end of the year for a new job.
His responsibilities will be taken on by British Gas marketing director Will Orr, insight director Julian Elliot and Chris Allin, director of loyalty and customer communications.
Last month it emerged British Gas was cutting almost 20% of its commercial staff, including marketing roles, within its services division, in a bid to reduce costs amid a difficult economic climate.
Jansen's promotion last June saw him effectively become the second-most powerful executive at the company with him still retaining ultimate control of sales and marketing decisions.
A spokeswoman said: "After more than three years at the helm of the company's marketing and commercial teams, Rick Vlemmiks has decided to leave British Gas.
"The whole British Gas business has been re-branded after more than 16 years under the previous identity.
"Rick also developed and led British Gas's partnership with Nectar, which has resulted in nearly four million British Gas customers joining the scheme, and one million new Nectar cards being issued.
"Working directly with Sainsbury's, Rick was also responsible for the successful launch of Sainsbury's Energy."
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