One of the rocks is between 950 and 2,100 feet across (290-650m) meaning it is categorised as a ‘medium’ asteroid.
The other is somewhat smaller, being between 400 and 850 feet wide (120-260 meters).
NASA are confident neither asteroid will hit Earth.
In a statement Lindley Johnson, a NASA planetary defence officer, said: “These asteroids have been well observed—once since 2000 and the other since 2010—and their orbits are very well known.
“Both of these asteroids are passing at about 14 lunar distances from the Earth, or about 3.5 million miles away, but small asteroids pass by Earth this close all the time.”
The first asteroid, named 2010 CO1, will pass closest to Earth early Saturday morning.
This is the larger of the two asteroids, though NASA counts both as ‘medium’ sized space rocks.
It will be followed by a second, dubbed 2000 QW7, which will be at its closest point to our planet at 0.54am on Sunday.
To be categorised as large by NASA an asteroid must be 0.6 miles (1 kilometre) across.
This is the point at which its collision with Earth is expected to have global consequences, rather than being a regional issue.
It last made a close pass by Earth in September 2000, when it was first identified by scientists.
After the weekend it won’t make another similar approach until 2038.
NASA tracks major asteroids in the vicinity of Earth to check whether they are likely to collide and cause damage.
However sometimes authorities are taken by surprise, particularly by smaller rocks.
NASA recently admitted it only identified an asteroid, 2019 MO, hours before it crashed into Earth.
The collision took place on June 29, with the asteroid burning up in the atmosphere above the Caribbean.
2019 MO was approximately 300,000 from Earth when it was identified by NASA.
This is further away from our planet than the Moon.
In a statement NASA claimed this was “roughly the equivalent of spotting something the size of a gnat from a distance of 310 miles”.
The asteroid was detected by the ATLAS survey telescope situated at the University of Hawaii.
In February 2013 as asteroid broke up over Chelyabinsk in Russia injuring 1,200 and damaging at least 7,000 buildings.
The asteroid in question was approximately the same size as a six-story building.