Kaye becomes chief executive, replacing Patrick Cairns who had decided to leave in the wake of the £10m deal, said the company.
Kaye joins Plum following two years as a consultant to food and drink companies. Prior to that he was managing director for UK foods at Dairy Crest, and he has also held senior roles at Mars, Heinz and Northern Foods.
Plum founder Susie Willis, the former chef and mum of three who launched the premium organic brand in 2006, remains as creative director.
The company, which supplies products to Tesco, Sainsbury's, Morrisons and Waitrose, as well as to Boots and Ocado, produces a range of about 50 meals and recipes that wouldn't look out of place on an adult menu, such as giant couscous with chicken, squash and red pepper. According to Darwin, the company is on course to deliver retail turnover of £15m this year.
Kaye said he was thrilled to be joining "the most dynamic and innovative babyfood business in the UK". "The opportunity is to continue to build on the work the team has already done and those opportunities are limitless," he said.
"We will first and foremost look to expand in the UK, building even further on our distribution and brand awareness, but we also believe there is a medium-term opportunity to expand overseas."