“Eleven members of an elite unit of the air force intelligence service and a (Russian-language) translator, led by an officer, infiltrated 3.5 kilometres (two miles) behind enemy lines in the Al-Atira region on Tuesday and recovered the airman,” the pro-government newspaper said.
Al-Atira is an area of Latakia province, around 12 kilometres (eight miles) from the border with Turkey.
Syrian forces launched the operation after Turkey downed the Russian jet on Tuesday morning, forcing the two-man crew to eject over rebel-held territory.
According to Al-Watan, the team set out in late morning from the Hmeimim airbase in Latakia, where Russian forces are concentrated.
The plane’s pilot had already been killed by rebel fire as he parachuted down but a Russian drone spotted navigator Konstantin Murakhtin in hiding on the ground.
The “Russian drone communicated to Syrian special forces the navigator’s location, as well as where the terrorist groups were,” Al-Watan said, referring to the rebels.
“He was spotted thanks to his GPS. It was a race against time because the terrorists were also looking for him.”
The paper said the special forces team used the codeword “Costa” for Konstantin, and the Syrian flag to identify themselves to the navigator as rescuers.
It said the rescue team clashed with rebels during the 12-hour operation, but were able to recover Murakhtin, who was injured in the leg.
Speaking to Russian state media on Wednesday, the navigator gave no details of his rescue, which the Russian military said involved its own special forces working alongside Syrian troops.
“I feel good in general. The military doctors work miracles,” he said, speaking at the Hmeimim base.
“I am waiting impatiently to be released by the doctors so I can immediately return to service.”
Russia has not released the name of the slain pilot, although President Vladimir Putin has said he will posthumously be given Russia’s highest award for valour, the Hero of Russia medal.
His body is believed to still be in the hands of rebel forces in Latakia province.
Murakhtin is also to be decorated along with soldiers involved in the rescue operation, including one Moscow has said was killed when his Mi-8 helicopter was forced to make an emergency landing after being hit by gunfire.