“The Final Problem” appeared in the December 1893 issue of The Strand. It was also the last story in the collection The Memoirs of Sherlock Holmes, published on December 13, 1893, by George Newnes of London.
Readers did not take Holmes’s demise very well. A Curious Collection of Dates: Through the Year with Sherlock Holmes, by Leah Guinn and Jaime N Mahoney, quotes this passage from the Manchester Courier and General Lancashire Advertiser (December 30, 1893):
If […] Dr. Conan Doyle has some new vein [of gold] to work, well and good. We question if he can improve on Sherlock Holmes. But if not, he must resuscitate his hero, for we simply do not know what the reading public will do without him.
[A Curious Collection of Dates is a really remarkable book and a great read. –Chips]