The deal will enable Finsbury to push forward in the premium and celebration cake sectors, broaden the company's product portfolio and provide the group with a good platform from which to target European markets.
Finsbury chief executive Dave Brooks said: "The opportunities for the new Group are excellent, and with the acquisition we will have a scale where we can drive our premium agenda with all of our major customers."
UK bread and cake markets are together worth over £4.5bn (€6.7m). According to Mintel, the ambient cake market sees 3 per cent growth per year and was worth £1.47bn (€2.2bn) with particular growth in the premium goods sector last year.
Lightbody, which recorded a turnover of £24,434 (€36,911) in the six months ending 31 October last year, produces chocolate enrobed cakes, cereal snacks and bite-sized cakes.
The company has operations in Scotland and France and owns licenses to manufacturer Disney and Thorntons character cakes.
Lightbody managing director Martin Lightbody said: "We have watched the strong growth and performance of Finsbury and believe that we will make a perfect partnership given the alignment of our strategic vision, and that together we will be able to drive sales of UK multiple grocers' premium brands and deliver even greater growth for our key licensing partners."