Morsi, in a televised speech, also acknowledged he has made mistakes since his election and called on opposition leaders to join in a dialogue on the country's future, the Qatari broadcaster al-Jazeera reported.
"The coming days will witness, God willing, the launch of new projects ... and a package of incentives for investors to support the Egyptian market and the economy," he said.
Ahram Online reported Morsi signed the document, which the Supreme Electoral Commission said was approved by 63.8 percent of voters in balloting the past two Saturdays.
The constitution was drafted largely by Muslim members of the Constituent Assembly. Opponents say it mixes politics and religion and have organized street protests against it. Morsi, however, said the document protects minorities sufficiently, denouncing the opposition as creating unnecessary turmoil.
Mohamed ElBaradei of the National Salvation Front, a former head of the U.N. nuclear watchdog agency, said the new constitution is an "interim" document. He said a new one should be drafted with contributions from all sides.
Both a U.S. State Department spokesman and Catherine Ashton, the European Union's foreign policy chief, called on all parties to forgo violence and engage in dialogue, al-Jazeera said. Ashton pointed out that turnout was low for the vote on the constitution.
"President Morsi, as the democratically elected leader of Egypt, has a special responsibility to move forward in a way that recognises the urgent need to bridge divisions," Patrick Ventrell, acting State Department spokesman, said.