Webster, who will take on the job from 1 January, joined IPC in 1992 as a graduate trainee and has worked across its circulation and marketing departments before becoming publisher of IPC's specialist division.
She was appointed to the IPC board in 2003 as managing director of IPC's country & leisure division before she became managing director of its women's division, IPC Connect, which includes titles such as Woman, in 2004.
IPC has yet to name an executive to take over Webster's role of IPC Connect managing director.
Her promotion follows the departure of IPC's managing director of advertising, Caroline McDevitt, in November.
Webster will now combine McDevitt's duties as well as her new chief executive role.
Auton joined IPC in 1977 and was appointed chief executive in 2003. She will now be based in New York.
Auton said: "Although my US responsibilities mean I will be moving to New York, I will be returning to the UK regularly. IPC remains close to my heart and I am looking forward to continuing to work with Evelyn and the superbly talented IPC Media board to take this company to even greater heights."