Here's a link to a website that gives some history behind Memorial Day and yes we began to celebrate it during the 19th century. Memorial Day History The site also has a great list of referring sites as well.
In 1870 The Army produced a record of ceremonies over the graves of the fallen soldiers. The National Memorial Day
In 1897 Michigan produced a small book for a suggested program for their schools in observance of Memorial day. Memorial Day
Please note that the practice started in the South before it became a National holiday and it was commonly known as Decoration Day.