A on-site witness said the cargo ship was first centered in the canal and then start navigating north.
Other ships were moving subsequently while sounding their horns.
The SCA sent a total of 13 tug boats and two dredges for the rescue work, said SCA chairman Osama Rabie.
The rising tide helped with the tugging and pushing efforts of the ship, he said.
Egyptian President Abdel Fattah al-Sisi on Monday thanked "Egyptians who contributed technically and practically to ending the crisis of the Ever Given stuck in the Suez Canal" via a Facebook post.
The SCA chief sent a message of reassurance to the international maritime community that "navigation in the canal has resumed."
The 224,000-ton container had been stuck and blocking the vital waterway since March 23 after it lost the ability to steer amid massive winds and a sandstorm.
The incident caused a temporary suspension of navigation in the man-made canal, leaving more than 420 ships stranded.