The simple answer is that it's attested to relatively early sources that provide a reasonably convincing argument for its historicity. Michael Lecker (Hebrew U) is probably one of the foremost experts on the "constitution" working today, argues that:

The term “constitution” is, however, a misnomer because the document deals mainly with tribal issues, such as the organisation and leadership of the tribal groups that participated in the document, as well as warfare, blood money, the ransoming of captives, and war expenditure. ... The whole document originated at one time, and there are no cogent arguments for analysing it into several documents. Attempts to link various parts of it to certain events in Muḥammad’s life, in particular to his encounter with the Jews, are pure conjecture.

The document appears in its entirety in Ibn Isḥāq's biography (sira) of Muhammad, who dates it to after the hijra (622 CE); the document also appears in Abū ʿUbayd’s Kitāb al-amwā.

Since similar treaties were signed by the third caliph, Umar, with the Christians of Syria during his rule (634-644), we know that the document dates back at least that far, and it makes sense that Umar would have used the original as a template.

The quoted text above is from: Lecker, Michael, “Constitution of Medina”, in: Encyclopaedia of Islam, THREE, Edited by: Kate Fleet, Gudrun Krämer, Denis Matringe, John Nawas, Everett Rowson. Consulted online on 22 January 2020 http://dx.doi.org/10.1163/1573-3912_ei3_COM_24415.

Other references: Moshe Gil, The constitution of Medina. A reconsideration, Israel Oriental Studies 4 (1974), 44–66

Robert B. Serjeant, “The sunnah jāmiʿah, pacts with the Yathrib Jews, and the taḥrīm of Yathrib,” Bulletin of the School of Oriental and African Studies 41 (1978), 1–42

Michael Lecker, The constitution of Medina. Muḥammad’s first legal document, Princeton University Press, 2004

Saïd A. Arjomand, The constitution of Medina. A sociolegal interpretation of Muhammad’s acts of foundation of the umma, International Journal of Middle East Studies 41/4 (2009), 555–75.