The appointment of Hunt was confirmed today by Jana Bennett, director of BBC Vision, nine weeks after Fincham departed.
The appointment is a blow for Five, which only appointed Hunt in May to replace Dan Chambers. She joined Five from the BBC, where she was the corporation's controller of daytime and early peak television with responsibility for all output on BBC One and Two during the day, including 'The One Show'.
Explaining why she was leaving Five after less than six months, Hunt said the decision had been a difficult one.
"Controller of BBC One has always been my dream job. Ultimately, I could not resist the opportunity to take on such a creatively exciting role.
"It has been an incredibly difficult decision to leave my talented team at Five but I could not turn down the best job in television."
Last week, speculation centred on Former BBC Two controller Jane Root, who is returning to the UK from the US after leaving her role as president of Discovery Channel.
Fincham resigned in the wake of the media storm about the controversial programme trailer about the Queen. The first part of the programme, now called 'Monarchy: The Royal Family at Work', finally aired last week.
Bennett said: "I am really pleased to welcome Jay back to the BBC to take up the reins of the UK's most popular channel and the BBC's flagship channel. She has impeccable credentials as a commissioner, channel leader and journalist and has a deep commitment to the BBC's mission to bring the best programmes to the widest audience.
While controller of daytime and early peak, Hunt commissioned factual shows such as 'Great British Menu', 'Extreme Dreams', 'Heir Hunters' and the Royal Television Society award-winning 'Through Hell and High Water'.
She also brought consumer journalism back to daytime with hit programmes such as 'Don't Get Done, Get Dom', 'What's Really in Our Food?' and 'Shopping the Supermarkets'.
Hunt has spent most of her career at the BBC, having joined in 1989 as a researcher on 'Breakfast News' and worked her way up to output editor before joining 'Newsnight', where she stayed until 1998.
She then moved to 'Panorama' as a senior producer, becoming editor of the 'One O'Clock News' and then the 'Six O'Clock News'.
She will take up her new role sometime next year.
Lisa Opie, Five's managing director, content, said: "Jay has already achieved a great deal during her brief time at Five and the first half of 2008 is already scheduled and commissioned.
"She will be with the channel for a few months yet and we look forward to having the benefit of her enthusiasm and creativity until she leaves for the BBC.
"We know this has been a very hard decision for Jay to make and wish her all the best in her new role."
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