Tegu was founded in 2006 by brother Chris and Will Haughey, and launched its range of magnetic wooden construction blocks in 2009. They began to explore how they could modernize wooden blocks, which are a staple in classrooms, which led to the innovation of magnetized blocks.

The blocks are all proportionally scaled. The foundation piece is the cube, and the long plank in four times the length of the cube. The candy bar is half the height of the cube, and the length of the three cubes wide. The short plank is a quarter of the height of a cube and is two cubes wide. These corresponding proportions are meant to also introduce children to the concepts of fractions and aid them in early mathematics. The magnets are hidden in specific places within the blocks in order to aid play and fuel curiosity. The magnets are also oriented deliberately randomly, with some blocks were north faces out and some where south faces out. This is meant to encourage curiosity as the blocks variously repel and attract each other.

The company is named after Tegucigalpa, the capital city of Honduras. The blocks are made from sustainably harvested wood from Honduras and Guatemala. As of 2016 they had planted more than half a million trees, and the company donates revenue to support the replanting of trees. The Tegu reforestation programme pledges to plant at least one tree in Honduras per Tegu set which is sold. By sourcing sustainable wood, Tegu aim to reduce the illegal logging in Central America.