Tombazis graduated with a degree in engineering in 1989 at the Trinity College in Cambridge, followed by a PhD in aeronautical engineering at the Imperial College London in 1992.
In November 1992 he became aerodynamicist at the Benetton Formula 1 team and was promoted to Head of Aerodynamics in 1994. Three years later he moved to the Scuderia Ferrari, where, in 1998, he became Head of Aerodynamics and CFD. In 2004 he went back to England, to work with McLaren, where he started working in a similar position and being promoted to Head of Planning.
In March 2006 he was back at Ferrari, this time as Chief Designer. He left Ferrari on 16 December 2014.
On 15 January 2016, the Manor Formula 1 team appointed Tombazis as its chief aerodynamicist.
Following the closure of Manor he set up his own consultancy, called MAA, and has been a visiting professor of aerodynamics for Imperial College London.
On 6 March 2018 it was announced that Tombazis has joined the FIA to become its 'head of single-seater technical matters'.
- 1992–1993: Benetton Formula aerodynamicist
- 1993–1995: Benetton Formula chief aerodynamicist
- 1997: Scuderia Ferrari aerodynamicist
- 1998–2003: Scuderia Ferrari chief aerodynamicist
- 2004: McLaren chief aerodynamicist
- 2005: McLaren project chief director
- 2006–2014: Scuderia Ferrari chief designer
- 2016-2017: Manor F1 Team chief aerodynamicist
- 2018-present: FIA Head of Single Seater Technical Matters
Tombazis lived in Castelnuovo Rangone (Modena) together with his wife and four children. He then moved to Greece for three years. Following this period, the Tombazis family moved to Geneva (Switzerland), where he still resides, for his position at FIA. He is the son of one of the most important Greek architects, Alexandros Tombazis. In his free time, Tombazis has said that he enjoys sculpture and spending quality, creative time with his family, playing Catan and Monopoly.