The controversy sparked anger among many of the bank's staff and led to senior staff writing to its board complaining that the leadership crisis had undermined their work in combating corruption.
The scandal also damaged US relations with Europe, which led calls for his dismissal.
Wolfowitz, currently a defence and foreign policy studies scholar at the American Enterprise Institute, a Washington think-tank, served as deputy secretary of defence during much of Bush's presidency.
In his new position he will advise on several high-profile issues, including pending nuclear deals with India and North Korea and offers to negotiate with Iran over its controversial nuclear programme.
He will report to Condoleezza Rice, the US secretary of state.