Tl; dr: Not 100% guaranteed, but the current consensus seems to be Dynastic Founder Ímar (d. 873) of Uí Ímair dynasty in Ireland also involved with the activity of Great Army in England, thus the same person as a historical model of Ivar the Boneless in later sagas.

The real problematic part of the complexity on identification might rather be legendary Ívarr with the moniker of "Boneless (hinn Beinlausi in Old Norse") who appear in later Old Norse sagas as a son of Ragnar Lodbrok, a legendary Viking leader, with the historical Ívarr/ Ímar, founder of Uí Ímair dynasty, however, I suppose.

As for the latter historical Ívarr/ Ímar, contemporary British accounts state:

• Anglo-Saxon Chronicle (MS A: a. 878) mention that he had at least two more brother, Halfdan, one of the leaders of Great Army, and anonymous one killed in the battle in 878 (usually identified with Ubba since the 12th century, but we are not so sure - see the linked post below) (Swanton trans. 2000: 74, 76). This post-mortem allusion to him is indeed the only account on him in near-contemporary English sources, and their attention to him is really limited (probably due to the fact that Ívarr/ Ímar mainly involved with the English affairs between 866x870.
• There are two conflicting accounts of his obituary:
• Aethelweard's Latin translated version, Chronicon, of Anglo-Saxon Chronicle (Late 10th century) adds a notice that Ívarr was died in 870, the same year as the martyr of St. Edmund of East Anglia.
• Contemporary Irish annals (especially Annals of Ulster) record that Ímar still actively attacked Strathclyde in 870 and died in 873 as following: "Ímar, king of the Norsemen of all Ireland and Britain, ended his life (AU a. 873)."

While the objection on the identification of Ívarr/ Ímar is apparently based on the discrepancy of these two contemporary Irish and a bit later English accounts, the latter (English) one has generally got much less credence from recent scholarship (due to the late date as well as hagiographical character of the account in accordance with the development of St. Edmund cult in course of the 10th century. Thus, in the latest standard account of Uí Ímair dynasty, Downham mostly prefers the Irish accounts and concludes that Ívarr in England who had been active between 866x870 and "King" Ímar "of the Norsemen of All Ireland and Britain" whom the annals record his obituary in 873 CE was indeed the same person (Downham 2007: 64-67 & passim.). Hadley & Richards also apparently has almost no difficulty in identifying Ímar who had been active in Ireland around 860 with Ívarr who campaigned against the Strathclyde Britons in 870-1, and further, involved also with the Great Army (Hadley & Richards 2021: 8, 43, 80).

There have been considerable accumulation of recent scholarship on the Vikings' activity around the 9th century British Isles since 1980s, and Ó Corráin's article (Ó Corráin 1979) that wikipedia entry on Ímar belonged to the old generation prior to this surge of recent research. Ó Corráin himself proposes a new interpretation that connect Ireland and Scotland as a unified activity sphere of the Vikings around the middle of the 9th century onward (instead of the Viking attacks launching from Scandinavia) in 1998, though he does not mention the possibility of Ímar's activity in England in 860s (Ó Corráin 1998).

On the other hand, as for the development of legends on Ívarr and his alleged brothers and father, I hope the following previous answers might be interesting to you:

• /u/sagathain's anwer in How can Ragnar Lodbroks children be considered real historical figures, but Ragnar himself is still considered to be mostly fictitious?
• Ragnar Lothbrok, by far my favourite character in Vikings, but how much about him is true? Who were his actual sons? answered by /u/Platypuskeeper
• I also wrote something in Vikings and Ragna Lothbrok and his 5 sons, how accurate is the History Channel show?

References:

• Swanton, Michael (trans.). The Anglo-Saxon Chronicles: New Edition. London: Phoenix, 2000.

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• Downham, Clare. Viking Kings of Britain and Ireland: The Dynasty of Ívarr to A. D. 1014. Edinburgh: Dunedin, 2007.
• Hadley, Dawn M. & Julian D. Richards. The Viking Great Army and the Making of England. London: Thames & Hudson, 2021.
• Ó Corrain, Donnchadh. "The Vikings in Scotland and Ireland in the Ninth Century." Peritia 12 (1998): 296–339.