Mr Aingimea was elected in parliament after former president Baron Waqa lost his seat in Saturday's general election.
He named his cabinet Wednesday.
Mr Aingimea is Minister of Foreign Affairs and will hold a series of more minor portfolios.
All six of the other cabinet posts are filled by newly elected MPs.
They include Martin Hunt in Finance, Isabella Dageago as Health Minister and Maverick Eoe becomes Minister of Justice.