Mr Cochrane has backed a campaign launched by the Confederation of British Industry (CBI) today to make Europe more competitive at a time of emerging markets in Latin America, Asia and Africa and a resurgent United States fuelled by cheap shale gas.
Prime Minister David Cameron has promised a referendum on European Union membership - but not until after the next General Election in 2015.
Research by the CBI claims that EU membership is worth the equivalent of £3000 to every UK household.
Mr Cochrane, who heads a business with 15,000 employees and has operations in 70 countries, said: "Weir Group is in favour of the UK's continued membership of the European Union.
"It is a position based on economics not politics.
"The EU is not perfect and extending the single market across services and profession could add real value."
Ten months of research has gone into a CBI report, "Our Global Further: the Business Vision for a Reformed EU" which is published as the business lobby group meets in London for its annual conference.
It sets out the case for Britain remaining a full EU member and makes the case for the extension of the single market to more areas while arguing for the repatriation to nation states rules around labour markets.
CBI director general John Cridland said: "Membership of the European Union's single market remains fundamental to our economic future.
"There is a false premise that we either trade with Europe and have a political relationship with Europe or go on a mission to the rest of the world.
"In a globalized economy, British companies need to do both and they need to do them at the same time."
Only 6.8% of UK trade goes to the BRIC markets (Brazil, Russia, India, China) against 79% to the EU, United States and other developed economies, according to CBI figures.
The group therefore believes it is crucial that the UK benefits from the free trade deals the EU seeks to secure.
Mr Cochrane said: "The European Union is one of the cornerstones of UK competitiveness and the challenge has never been greater."
The emergence of cheap shale gas and oil has given American companies a competitive advantage, he said.
"It is important that Europe responds," Mr Cochrane added.
"This is an argument for the EU to perform better but not for the UK to withdraw from such a successful economic partnership."
He dismissed the idea of pulling out of the EU.
"At best we would be left on the fringes. At worst we would have to renegotiates deals with trading blocs that dwarf us," he said.
He noted the expense and time wasted by Weir Group staff getting their goods across borders in regions, such as Africa, where there is limited free trade.
The CBI insisted its drive for free market reform of the EU had backing in other member states, notably in northern Europe.
Mr Cridland, said: "We are better off in a reformed EU than outside with no influence. Each year, membership is worth £3000 to every household in this country.
"But the EU isn't perfect and there is a growing unease about the creeping extension of EU authority. Europe has to become more open, competitive and outward looking if we are to grow and create opportunities and jobs for all our citizens."
He said it was crucial that eurozone integration did not come at the expense of the interests of other EU states outside the currency bloc.
Douglas Flint, the Glaswegian who chairs HSBC bank said: "It is important that the product of this process of change in Europe is a stronger EU with Britain at its heart."