The firm was founded in London in 1946, as the Ove N. Arup Consulting Engineers by Ove Arup. He set out to build a firm where professionals of diverse disciplines could work together to produce projects of greater quality than was achievable by them working in isolation. In 1963, together with the architect Philip Dowson, Arup Associates was formed. In 1970, the firm reformed as "Ove Arup & Partners".
It is best known for its design work for the built environment. Projects to which it has contributed include the Sydney Opera House, which is largely credited with launching Arup into the premier league of engineering consultancies. The BBC and RIBA documentary The Brits who Built the Modern World highlighted Arup’s collaboration with architects and described Arup as "the engineering firm which Lord Norman Foster and his peers Lord Richard Rogers, Sir Nicholas Grimshaw, Sir Michael Hopkins and Sir Terry Farrell most frequently relied upon."
Arup had its own sports division, Arup Sport, specialising in designing, consulting and structural engineering for sporting facilities such as stadia. This group continues to work under the banner of Arup Associates following a streamlining of the Arup brand. Many of Arup's modern stadia are designed with a contemporary, distinctive edge and the company strives to revolutionise stadium architecture and performance. For instance, the Bird's Nest Stadium for the 2008 Olympics was complimented for its striking architectural appearance and the City of Manchester Stadium for the 2002 Commonwealth Games has stairless entry to the upper tiers through circular ramps outside the stadium. The most notable stadium projects led by Arup remain the City of Manchester Stadium (2002), Allianz Arena (2005), Beijing National Stadium (2008), Donbass Arena (2009) and the Singapore Sports Hub (2014).