As well as managing a multidisciplinary team of consultants and advisers, the job involves liaising with the planning authority, boroughs and the Greater London Authority as well as ensuring that the Olympic Park and other venues meet local communities' aspirations.
The ODA is looking for someone with a track record of promoting, delivering and implementing multi-million pound projects to budget and deadline. The closing date for applications is 18 May.
Meanwhile, Network Rail chief executive John Armitt was named as the new ODA chairman this week. Acting chairman Roy McNulty will become deputy chairman after Armitt takes up his post from September.
Armitt said the ODA has made a "very good start" to delivering the games. "I look forward to providing leadership as the programme moves to the next stage," he added. His appointment follows last year's departure of former chairman Jack Lemley, who claimed that political wrangling was delaying the project.
Selina Mason, director of architecture and design review at the Commission for Architecture and the Built Environment, is also set to join the ODA. She will become deputy head of design from August, responsible for securing design quality across the entire Olympic development.