Many of the signers of the Constitution, as well as the signers of other early American legal documents, were lawyers. And many of the others had studied law.

They were familiar with the legal history of Europe, including such landmark legal documents as the Magna Carta. They also studied Greek and Roman philosophy, and its ideas of "natural law," which is where John Locke got a lot of his ideas in the 1600s. Locke's philosophy, as well as those earlier philosophies, were influential on Thomas Paine's writings which were, in turn, influential in the writing of the Declaration of Independence.

Great Britain doesn't have a formally written constitution, but it still has a constitution--it's just the collection of laws passed by Parliament that haven't been overturned, and judicial decisions handed down by the courts ("common law"), as well as outstanding precedent. Each of the colonies had a charter of rights, which were the predecessors of their state constitutions. The way these colonial charters fit within the structure of the English constitutional system was one of the main sticking points that led to the Revolutionary War--did British Parliament have the right to revoke these charters unilaterally like they did to Massachusetts under the Intolerable Acts, or was Parliament legally obligated to get permission from the colony's legislature to revoke the colony's charter?

When writing the U.S. Constitution, since Great Britain did not have a formal constitution of their own, the Founders relied heavily on the multi-volume Commentaries on the Laws of England written by Sir William Blackstone, which collected the most important acts of Parliament and judicial common laws into a single work. The book was referenced from time to time in the writings of the Founders. Among other places, John Adams wrote about it in his diary, Alexander Hamilton mentioned it in Federalist Paper No. 84, and James Madison listed it among the books for use by Congress when the Revolutionary War was ending and Congress was going to soon be debating how to replace the Articles of Confederation with a more permanent and sturdy document outlining the rule of law to govern the new country.

The first three sections of the introduction to the first volume of that book, encompassing nearly a hundred pages, give an overview of the origins of the written law and legal philosophy in Europe going back to Greek and Roman times, and the origins of constitutional laws of England more specifically. Many if not most of the founders would have been familiar with the ideas discussed in these sections before Madison told them they should read this book. And any founder who wasn't familiar with them would have been treated to this cursory overview if they had taken Madison's advise and read it. Madison was certainly familiar with all of it, and he is often called "the Father of the U.S. Constitution." He had actually been assigned to read the book when he was studying to become a lawyer in the early 1770s, and there's no doubt that many of the other founders with legal backgrounds were already familiar with it before Madison put it on his "recommended reading" list.

There are also other books there on Madison's recommended reading list that deal with European law, English law, natural law, and legal philosophy. These were all subjects that the writers of the Constitution were deeply familiar with.

If you want a more in-depth study on all this, I recommend reading The Origins of the American Constitution: A Documentary History by Michael G. Kammen. It will give you much more detail about the specific origins of each section of the Constitution, but in general, the Constitution was based on what was learned in a legal education of the time, which included the study of European legal philosophy dating back to classical Greece, as well as the informal English constitution, particularly as compiled in Blackstone's Commentaries.