The Arba'een pilgrimage has been observed since the year 61 AH of the Islamic calendar (10 October 680) after the Battle of Karbala or the following year. According to tradition, the first such gathering took place when Jabir ibn Abd Allah, a sahabah, made a pilgrimage to the burial site of Hussain.
In fact, Jabir is considered the first one who visited the tomb of Imam Hussain. He was accompanied by Atiyya ibn Sa'd because of his infirmity and probable blindness. His visit coincided with that of the surviving female members of Prophet Muhammad's (saaw) family and Imam Hussain's (s) son and heir, Imam Zain-ul-Abideen (as), who had all been held captive in Damascus by Yazid, the Umayyad Caliph.
Jabir ibn Abdullah al-Ansari stood at the grave and burst in tears then thrice called out al-Hussain’s name, then he said, "Why a loved one does not answer one who loves him?" But soon he answered his own query by saying, "How can he answer while his cheeks are torn and his head is separated from his body? Yet I testify that you are the son of the Seal of Prophets (saaw), the son of the master of the faithful (as), the son of the inseparable ally of piety, the descendant of guidance, the fifth of the fellows of the kisa’, the son of the master of naqeebs, the one who was brought up in the lap of the pious, that you were raised on the milk of iman, that you were weaned with Islam, so you were good when you were alive, and you are so when dead. But the hearts of the faithful are not pleased with parting with you, nor do they have any doubt about goodness being yours. So peace of Allah be upon you and His Pleasure. And I bear witness that you treaded the same path treaded before you by your brother [prophet] Zachariyya (Zacharias)."
Having said so, Jabir turned his head around the grave as he said, "Assalamo Alaikom, O souls that abide at al-Hussain’s courtyard! I bear witness that you upheld the prayers and paid the zakat, enjoined what is right and prohibited what is wrong, struggled against the atheists and adored Allah till death overtook you. By the One Who sent Muhammad, peace of Allah be upon him and his Progeny, as His Prophet sent with the truth, I testify that we have a share in what you have earned." Atiyyah al-'Awfi his companion who was leading him, since he, a maternal relative and one of the greatest sahabis of Prophet Muhammad (saaw), as indicated above in a footnote, was by then a blind old man] asked him, "How so when we did not descend upon a valley nor ascend a mountain, nor did we strike with a sword, whereas the heads of these people have been severed from their bodies, their sons have been orphaned and their wives widowed?" Jabir answered: "I heard the Messenger of Allah (saaw) whom I very much love saying, One who loves a people will be lodged with them, and one who loves what some people do will have a share in [the rewards of] their deeds.’ By the One Who sent Muhammad (saaw) as a Prophet with the truth, my intention and that of my companions is similar to that for which al-Hussain (as) and his companions were all killed."
SOURCES:
1. Wikipedia (https://en.wikipedia.org/wiki/Arba%27een)
2. The Book "Karbala and Beyond" by author Yasin T. Al-Jibouri. (https://www.al-islam.org/karbala-and-beyond-yasin-t-al-jibouri)