Senior members of the moderate Islamist Ennahda Party said the wording of the old constitution, which proclaims Islam as the state religion, would remain.
A group of ultra-conservative Muslims known as Salafis had demanded the introduction of Sharia.
Ennahda has been under growing pressure to declare its position on the issue.
The BBC's Jon Leyne says that the news will disappoint the increasingly vocal conservative minority, but it will bring relief to liberals and secularists who fear a tide of Islamism sweeping across the region.
"Ennahda has decided to retain the first clause of the previous constitution without change," senior Ennahda official Ameur Larayed told local media.
"We want the unity of our people and we do not want divisions."
The article from the 1959 constitution states: "Tunisia is a free, sovereign and independent state, whose religion is Islam, language is Arabic and has a republican regime."
Another senior figure, Ziad Doulatli, said he hoped the decision would help Tunisia to "serve as a model for other countries going through similar transformations".
Some 10,000 Salafis took to the streets of the capital, Tunis, on Sunday to express their support for the proposal that the country's legislation should be based on Islamic law.
The Tunisian uprising last January, which unseated long-time President Zine el-Abidine Ben Ali, inspired a wave of pro-democracy movements across North African and the Middle East.
Officials from the largest party in Tunisia's governing coalition have said they will not support moves to enshrine Islamic law in the new constitution.