Tavner took the reins at Woman's Own in 1998 after its former editor Keith McNeill died. Before this, she edited Eva and Chat and has been at IPC since 1989.
IPC remained tight-lipped about the reason for Tavner's departure and whether she had a new job to go to.
In a statement, IPC Connect managing director Linda Lancaster-Gaye thanked Tavner for her "hard work and commitment to the title".
One reason for Tavner's departure could be the title's declining circulation, which she failed to halt.
When Tavner joined Woman's Own, the title had a circulation of 653,000, down from the previous year's 800,000. In the last set of ABCs, it had a circulation of 538,424 for the January-July 2001 period.
However, the whole market has suffered from increased competition in the sector so there is still speculation as to whether this is the reason for her departure.
Tavner's replacement McAlanon joined IPC in 1997 as deputy editor of Marie Claire and was responsible for persuading Monica Lewinsky to pose for the front cover.
She then moved to edit the 74-year old, now defunct, Woman's Journal, which was axed in November along with a number of other titles as IPC sought to cut costs in response to the global advertising downturn.
McAlanon said: "Taking over as editor of such a well-known magazine is a huge challenge and one that I am extremely excited about. I believe the weekly market is the place to be right now and I welcome this fantastic opportunity to use my experience to expand and develop Woman's Own."
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