The 48-year-old who, after chairman Tim Delaney, was the most senior person at the agency until his resignation earlier this month, said the move was a result of his "need to feel challenged".
Martin Lambie-Nairn, the chief creative director and the founder of Lambie-Nairn, said: "Nick brings years of experience from both advertising and marketing, which will help us create new opportunities and ensure the continued success of our business."
Hough takes up the post on 1 September.
Lambie-Nairn was founded in 1976 and specialises in developing creative and pan-media branding solutions throughout the broadcast, financial services and telecommunications markets.
The agency has a prestigious client list, with the famous BBC2 idents, the launch of Channel 4 and, more recently, the branding of the mobile phone network O2 among its achievements.
It was also responsible for creating the youth digital channel BBC3's "blobs" and also developed O2's image and position with the creation of the "bubbles" concept.
Hough joined Leagas Delaney in 1998, initially as the UK managing director following a three-year spell overseas with Lowe in Amsterdam, where he was also managing director.
His career has included stints at Leo Burnett and BMP DDB after he started out with J.Walter Thompson in 1980.
He said: "I had been thinking for some time about what to do next. Lambie-Nairn is an extremely interesting business with a great creative reputation.
"For many years, it has been comfortably the best in the field of broadcast identity. I believe that the agency has enormous potential in its heartland business and I look forward to taking it further," he added.