At a ceremony in Khartoum's Republican Palace, Beshir hailed the fact that the National Constitutional Revision Commission (NCRC) unanimously agreed on the new basic law.
"The passage of the draft constitution unanimously without the need for vote-taking among the NCRC transmits a message to the world that the Sudanese people are tolerant and are capable of putting past grievances behind, however severe they were," he said.
The 60-member NCRC includes a majority of representatives from the ruling National Congress and a little less than a third of former southern rebels from John Garang's Sudan People's Liberation Movement, with whom Beshir's government signed a peace agreement in Kenya in January.
The rest of the seats were given to opposition members, including from the National Democratic Alliance, which ended a 16-year feud with Beshir's regime by signing a reconciliation deal in Cairo last week.
The six-year interim period which is due to kick off with an official ceremony in Khartoum on July 9 will lead to a referendum on self-determination for the South.
The January peace deal ended a 21-year conflict pitting the mainly Christian and animist south against the Muslim and Arab-dominated central government. The war left an estimated 1.5 million people dead and displaced another four million.