The plaque has been erected at the father and son's former home at 49 Kew Green to celebrate their work in establishing the gardens. Sir William Hooker was the first director to live in the house - since inhabited by 14 directors and their families.
He was appointed director of the newly nationalised Botanic Gardens in 1841 and during his 24 years in service he increased the size of the garden from eleven acres to 75 acres of botanic garden and 270 acres of arboretum and pleasure grounds.
He is responsible for the lake, avenues and vistas and built more than 20 glasshouses, including the Palm House. He is also celebrated for increasing visitor numbers from 9,000 in 1841 to more than half a million by 1865.
Sir Joseph Hooker classified the plants his friend Sir Charles Darwin had gathered in the Galapagos, as well as making an expedition to the central and eastern Himalayas, from where he sent back around 7,000 fauna specimens to Kew.
Following his father's death in 1865, he became director of Kew Gardens and was later elected as President of the Royal Society in 1873. English Heritage historian Esther Godfrey said: "We are delighted to commemorate the formidable partnership of this father and son."
Kew director Professor Stephen Hopper added: "We have an enormous amount to thank William and Joseph Hooker for and we are incredibly proud that they are so closely associated with Kew. Without them, it would not be the globally renowned organisation it is today - offering beauty and tranquillity to visitors while delivering first-class plant science research and conservation worldwide."