The Enstone-based team, effectively run by executive adviser and former principal Flavio Briatore who will continue to have overall charge, said Nielsen would start work as managing director on September 1st.
Nielsen has most recently been working for Liberty Media-owned Formula One, after a brief period as sporting director at the governing FIA.
He was also sporting director when Renault won championships in 2005 and 2006 under Briatore.
Alpine, last in the constructors' championship but switching to Mercedes engines next year, also appointed Kris Midgley as head of aerodynamic development.
Midgley previously worked at Ferrari as principal aerodynamicist and is also returning to the Enstone factory after a stint from 2007-13.
Oakes, the team's fifth boss in four turbulent seasons, resigned in May for personal reasons after being appointed in July last year.