For years, Khartoum's Islamist regime maintained close relations with Riyadh's arch-rivals in Tehran.
But as sectarian divisions in the region escalated with the conflict in Syria, Khartoum allied with Riyadh.
In 2015 it said it would take part in a Saudi-led military intervention in nearby Yemen against Iran-backed rebels.
"The air force drill showed that relations between Sudan and Saudi Arabia are progressing," Bashir said during a ceremony at the Meroe air base, 350 kilometres north of Khartoum, to mark the end of 12-day drill.
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Sudan took part in the exercise with more than two dozen fighter planes including MiG-29s and Sukhoi jets, defence officials said.
Saudi Arabia sent F-15 fighter jets and Eurofighter Typhoons.
Bashir said the Sudanese military was playing a "key role" in improving Khartoum's ties with Saudi Arabia and other Gulf countries.
"As Sudanese security is connected with that of countries across the region, we are building military and security cooperation with our neighbouring countries," said Bashir, who wore a military uniform for the ceremony.
Sudan is keen to ease its international isolation and Saudi Arabia is looking for avenues for investment to reduce its dependence on oil.
Saudi fighter pilots are set to stage an air show in Khartoum from April 10 to 12.
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