Mursi, in a televised address to the nation, called on Egyptians to work for stability and security of the country.
The constitution had been chosen by the people "with their own free will" in a referendum that was "totally transparent and supervised by the judiciary and monitored by NGOs", Mursi was quoted as saying by BBC.
He said the passing of the constitution meant Egypt could now move to a new stage that should bring security and stability for the people.
Mursi said he accepted the rights of those who opposed the constitution but also condemned those who he said had resorted to violence.
Mursi admitted mistakes had been made but insisted he would never make a decision except in the interests of the country.
Earlier in the day, Egypt adopted the constitution after a two-thirds 'yes' vote in a polarising referendum.
Some 63 per cent backed the constitution in the controversial referendum.
Mursi last night signed into law Egypt's post revolution constitution after the election authorities declared it overwhelmingly approved in a two-stage referendum that was held on December 15 and 22.
The opposition claimed the new charter compromises the country's secular character and is too Islamist. MORE
