''It's a wonderful opportunity. I'm very excited,'' she said.
''Jobs like this don't come up very often.''
Ms Wigley, who finishes work in Dunedin on September 27, will start her new job on October 7.
Voyager, like Toitu, is planning a refurbishment.
Ms Wigley has been Toitu director since March 2009.
The four-stage $37.5 million redevelopment of Toitu started in 2008 and the museum reopened in December last year. More than 200,000 people have visited the museum since then.
''I've actually created my ideal museum here. It has been a big, multilayered project and very successful.''
The Toitu redevelopment was a ''unique'' project, she said.
''We were able to start from scratch. We have fantastic collections, two heritage buildings and two new buildings - those considerations have huge challenges.''
With the available budget, ''something special'' was built. The next director would need to continue Toitu's evolution.
''There is always things to do in museums. It never stops and it will continue on growing and developing because museums are not static.''
The biggest challenge for a director was keeping a museum exciting and dynamic by constantly changing.
''And continuing to be relevant and building collections that are meaningful to the city. To ensure that people come back time and time again. To make sure there is always something new for them to see.''
The repeat visitors to Toitu showed it was up for the challenge, she said.
Working at Voyager would continue her maritime interest. She had worked for the National Waterways Museum in England and lived on a canal boat in central London.
''I do like boats and sailing. I used to live on a boat for about three and a-half years and I've helped restore boats in the past, so I have an affinity with the water.''
Dunedin City Council city strategy and development general manager Sue Bidrose said Ms Wigley could depart with her ''head held high'' after leaving the city with a world-class social history museum.
Dr Bidrose said an acting director would be appointed next month while the council considered a permanent replacement.
