In the book of Misbahul Motahajjid, Sheikh Toosi (RA) wrote: The twentieth Day of the Month of Safar 61 AH (After Hijra), is the day that Jabir ibn Abdullah Ansari (RA) a companion (Sahabi) of the Prophet of Islam (PBUH) came from Medina to Karbala for Ziarat of the grave of the third Shia Imam, Hussain ibn Ali (AS); and he was the first person who performed Ziarat of Imam Hussain (AS).
According to an article by En.shafaqna.com, it is Mostahab (recommended) to perform Ziarat of Imam Hussain (AS) on this day and this is called Ziarat Arbaeen.
Therefore, the tradition of Ziarat Arbaeen established by Jabir ibn Abdullah (RA).
Source:
Misbahul Motahajjid, Sheikh Toosi (RA).