[1] He was previously a member of the Legislative Assembly of Queensland from 2012 to 2016 and was Minister for Agriculture, Fisheries and Forestry under Premier Campbell Newman.

[2] His father Tom McVeigh was a federal Nationals MP from 1972 to 1988 for Groom and its predecessor, Darling Downs, and served as a minister in the Fraser government.

[2] He began his PhD in 2005 through the Cooperative Research Centre for Irrigation Futures and was awarded the degree in 2012, by which time he had become state agricultural minister.

His thesis was titled "Influencing sustainable water use in Australian irrigated agriculture: a value chain management approach".

[8][9] In April 2016, McVeigh won LNP preselection for the Division of Groom, which his father had held 30 years earlier.

[12] Following a ministerial reshuffle in December 2017, McVeigh was promoted to cabinet as Minister for Regional Development, Territories and Local Government.

[16] After leaving parliament, McVeigh was appointed director of the University of Southern Queensland's SQNNSW Innovation Hub and chair of the Regional Economies Centre of Excellence.