Rayyanah Barnawi, who is set to become the first Saudi woman in space, and Ali Al Qarni are due to launch on May 22, at 1.27am GST, from the Kennedy Space Centre in Florida.
This means there will be three Arabs in space together at the same time – a record number.
“Following in Prince Sultan bin Salman Al Saud's pioneering footsteps, two Saudi astronauts will launch on their first mission to the ISS and three Arab astronauts will be in space together,” Dr Al Neyadi tweeted on Sunday, along with the image of the kingdom.
“As we wish them a great launch, here's a recent view of Saudi Arabia I took.”
Prince Sultan became the first Arab in space when he launched on Nasa's Space Shuttle in 1985.
But the kingdom did not set up a long-term space programme after his return.
Saudi Arabia has recently renewed its interest in space exploration, having announced a sustainable astronaut programme last year.
Ms Barnawi and Mr Ali Al Qarni are the first Saudis to go to space since Prince Sultan's trip nearly 40 years ago.
They are expected to do 14 experiments assigned to them by Saudi researchers, and Dr Al Neyadi has been making preparations to welcome them.
On Friday, he spent the afternoon reviewing procedures and training on a computer for the approach and docking of the Saudis' Ax-2 mission.
He also set up computers in the cupola, the observatory on the space station, and the Destiny laboratory module, both of which will help to support the Ax-2 mission's arrival.
Last month, Dr Al Neyadi and his colleagues relocated a Dragon spacecraft to another docking port on the ISS to help free up a parking spot for Ax-2 and a cargo mission arriving in June.