The Grimm brothers spent their whole lives together and naturally they died in the same place as well. Wilhelm Grimm, who had spent most of his life being ill, died of an infection in 1859, at the age of 73. Jacob Grimm became a retired recluse shortly after his brothers death and eventually died of natural causes in 1863, at age 78. He worked everyday to then end of his life and stated this in his autobiography.

"Nearly all my labors have been devoted, either directly or indirectly, to the investigation of our earlier language, poetry and laws. These studies may have appeared to many, and may still appear, useless; to me they have always seemed a noble and earnest task, definitely and inseparably connected with our common fatherland, and calculated to foster the love of it. My principle has always been in these investigations to under-value nothing, but to utilize the small for the illustration of the great, the popular tradition for the elucidation of the written monuments."

Both brothers were buried at Alter St.-Matthäus-Kirchhof (Old St. Matthews Courtyard) in Berlin, Germany. A cemetary started in 1856 by the prostant parish of St. Matthew.

https://www.britannica.com/biography/Brothers-Grimm

https://www.newworldencyclopedia.org/entry/Jacob_Grimm