The Thirsk-based company is the UK’s largest independent manufacturer of dry pet food and has doubled in size over the last five years.
The family-owned firm, a leading supplier of the Big Four supermarkets, is aiming to win new contracts and expand into new markets in Britain and overseas.
Mr Lambert, the former chief executive of R&R Ice Cream, has joined the board as a non-executive director and will become non-executive chairman next March when Bill Page turns 75.
Mr Lambert told The Yorkshire Post: “It’s growing fast, it has a fantastic mill and the quality of its brands is getting stronger and stronger. The family has stuck together and created a wonderful business.”
Wagg is led by managing director Richard Page and his two brothers Tom and George. Their father Bill founded the business in 1990.
Wagg has invested £20m on automation at its manufacturing facility over the last four years to make the business as efficient and low cost as possible.
Turnover has grown to £58m this year, up from £22m in 2008. The company delivered core earnings of £9m this year and employs 125 people.
Richard Page said Mr Lambert has the skills to help the company take advantage of opportunities that may arise in the pet food industry, including consolidation in a tough retail market.
He added: “There’s undoubtedly a number of companies within the European context that are thinking about a sale.”
Wagg is wholly owned by the Page family and has minimal debt on its balance sheet, which means it could easily raise finance to fund any acquisitions.
Mr Page said the company is conservative by nature but would “think more laterally about ownership” if the right growth opportunity came up.
Wagg supplies Tesco, Asda, Sainsbury’s and Morrisons as well as the likes of Amazon, B&M and Poundstretcher.
Its brands - Wagg and Harringtons - make up 85 per cent of sales, with the remainder coming from own-label products.
The company has a small but growing export business supplying customers in Canada, Germany, New Zealand and Hungary.
At R&R, Mr Lambert transformed an old Victorian dairy with a small contract to supply Morrisons into Europe’s largest own-label ice cream maker via a series of mergers and acquisitions in a fragmented sector that was ripe for consolidation.
Like R&R, Wagg aims to grow its own-label manufacturing business to boost volume and keep its costs down.
Mr Lambert said: “In the grocery market, the people that are growing are the low-cost producers that are sustainable and can innovate and carry on investing.”
Another similarity is the sector, which has a lot of players and is dominated by two giants, in this case Pedigree and Nestle.
Mr Lambert expects to see some consolidation at some stage in the future.
He stood down as chairman of R&R this summer, a year after the buyout by French private equity house PAI Partners.
Mr Lambert is also chairman of Burton’s Biscuits, which owns the Maryland, Jammie Dodgers and Wagon Wheels brands and is backed by the $140bn Ontario Teachers’ Pension Plan, and vet drugs maker Animalcare plc.
Mr Page described his appointment at Wagg as “a momentous change” for the business.
He said: “On the one hand, we are all sad to see Father retire.
“He was instrumental in founding Wagg Foods and building it up to what it is today: the UK’s largest independent manufacturer of dry pet food.
“He had the vision and drive to create the current platform and everyone at Wagg is grateful for the opportunity this has given us.
“Looking forward, as markets become more challenging and opportunities for growth change, we are very fortunate to have someone with the calibre and experience offered by James to replace him.
“We are all looking forward to the new challenges and welcome James on board.”