A security source told the Egyptian website the seven were released in the desert about 43 miles from el-Arish. They were flown to Cairo on a military helicopter.
There were no details of negotiations that led to the release.
On hearing of their release, Morsi, who refused to negotiate with the kidnappers, thanked the military and intelligence forces for securing the release of the seven.
Morsi's comments were posted on his Twitter account, the site said.
The Egyptian president also thanked residents of the Sinai Peninsula for "their patriotic stance and for putting the nation's interest above all," the site said. "Long live Egypt. I am waiting for the arrival of my sons," he was quoted saying.
Egyptian authorities have reopened the Rafah border crossing with Gaza. Colleagues of those captured closed the crossing to protest last Thursday's kidnapping and refused to open it until the seven were released.
Seven servicemen were taken at gunpoint as they traveled between el-Arish and Rafah. Initial reports suggested they had been abducted by a jihadist group that demanded the release of jailed members of the group.
Security in the Sinai Peninsula has deteriorated since the ouster of former President Hosni Mubarak.