The new charter commits Poland to a market economy and private ownership, guarantees personal freedoms necessary for entrance into the European Union and ensures civilian control of the military necessary for Nato membership.
Polls leading up to the referendum indicated that most voters favoured the new charter, but the referendum campaign has emphasised traditional political divisions.
In the last major political confrontation before legislative elections in September, right-wing parties - including Solidarity - are calling on supporters to reject the charter passed by the left-wing parliament.
Some 28 million people are eligible to vote on the charter. Early results based on exit polls were to be released after voting closed at 10pm, but official results were not expected until late today or early tomorrow.
President Aleksander Kwasniewski, who led parliament's constitutional committee for two years before being elected president, has been one of the charter's chief backers, saying it will usher in political stability.
Right-wing parties, who found themselves outside parliament after the 1993 legislative elections, criticise it mostly on moral grounds. Solidarity, the former trade union that led to the fall of the communist regime in 1989, wanted the charter to state that God-given law, or a universal set of values, was higher than any law made by men.
In a gesture to the church, the charter guarantees protection of human life, but it does not specifically ban abortion. It also outlaws homosexual marriages and guarantees the right of religion classes in schools.