Mr Moore is to become the Deputy Prime Minister's new adviser on European business - charged with speaking to business leaders who are concerned they may have to move their operations elsewhere in Europe if Britain leaves the EU.
The MP - who was sacked as Scottish secretary in the last reshuffle - will report back to Mr Clegg before next summer's recess. He will not be paid for the job.
The appointment comes as the European Union (Referendum) Bill, proposed by Tory backbencher James Wharton, continues its passage through the House of Lords.
The legislation, which would see a referendum on the UK's membership of the European Union in 2017, has the support of Prime Minister David Cameron. But it faces opposition from peers, who may try and scupper the legislation by using up its allocated parliamentary time with long speeches on numerous amendments.
Even so, several business leaders have warned a referendum would create severe uncertainty and could lead to them moving their operations to other parts of the EU. Last month, Carlos Ghosn, chief executive of Nissan, said the company would re-evaluate its position if the UK was to leave the EU.
A Lib Dem source said Mr Moore would be speaking to other business leaders like Mr Ghosn, who were worried about the impact of the UK leaving the EU.
He said: "At the moment there are a number of business owners and leaders who are concerned about some of the discussions and rhetoric around leaving the EU and the impact it would have on businesses and jobs in the UK.
"Nick has been picking up on that and he felt it was appropriate to talk about those concerns. He has said that for too long we have let the narrative on Europe be anti-Europe.
"We are only a small party but it has reached the point now where Labour keep twiddling their thumbs and are not coming forward, while pro-European Tories have been brow-beaten and are too scared to say anything.
"We need to do this now. The more we talk to businesses, and there are some very, very high profile businesses and organisations, we are hearing that the positive economic arguments for remaining part of the European Union need to be put forward."
In a statement, Mr Clegg said Mr Moore's background made him the right MP for the job.
He said: "As someone with a background in European policy issues, a strong track record in engaging business when he served in the Cabinet and, importantly, a private sector career before entering politics, I have no doubt that (Mr Moore) will be a valuable part of the Government's efforts to create a stronger economy at the same time as we re-examine and underline the importance of the UK's economic ties with the rest of Europe."
Mr Moore said: "Britain's engagement with the rest of Europe is fundamental to our future economic well-being. At a crucial moment in the development of the UK's relationship with the European Union, I am delighted to take on this role to engage with UK businesses."