The Jersey Evening Post has reported the 12-month contract comes with a salary of £225,000.
A statement from the Government of Jersey said Mr Martin will be joining the Government on March 1, 2021, following his arrival in Jersey and his receipt of a negative coronavirus test.
Mr Martin joined Wandsworth Council in 2010, and since 2016 has also been Chief Executive of Richmond Council as part of the shared staffing arrangement between the two councils.
Mr Martin originally announced he would be stepping down from Autumn 2020, however this was delayed to lead the emergency response to the pandemic.
Proposals will be made to both full councils that Mark Maidment, the Director of Resources and Deputy Chief Executive, will step-up as interim Chief Executive during the recruitment process.