Kokorin, who was named by the 2018 World Cup hosts in the squad for friendlies against South Korea and Iran this month, had not been called up since November 2016.
"It's a good feeling, I'm glad to be back," the 26-year-old, who has 15 goals in all competitions this season and is currently the Russian Premier League's top scorer, said in a video posted on the national team's Twitter account.
"I missed (playing for the national team), lots of time has passed. Playing for a club is one thing, but it's completely different with the national team."
Over the past year Kokorin has made more headlines for incidents off the pitch than for highlight-reel goals.
But the striker, who had been a regular national team starter, is on the road to redemption with strong performances for Zenit this season, scoring eight goals in 12 domextic league matches to help the club top the table.
Kokorin and Russia team mate Pavel Mamayev were demoted to their respective clubs' reserve teams last year after footage of them at a champagne-fuelled party in Monaco emerged online following Russia's early exit from the European Championship.
Kokorin stirred more controversy in June by posting a video on Instagram in which he and Zenit team mate Artem Dzyuba seemed to be mocking national team manager Stanislav Cherchesov after Russia's elimination from the Confederations Cup in June.
The incident sparked speculation that Kokorin could be barred from the squad under Cherchesov, who was appointed in the aftermath of Russia's Euro debacle.
"I don't think much has changed, I know everyone here," Kokorin said of the national team. "Maybe there are some new rules I will be told about."
Russia will play a friendly against South Korea in Moscow on Saturday before hosting Iran in Kazan on Oct. 10.
Russia will stage the World Cup in 12 venues spread across 11 cities including Moscow, St Petersburg, Kazan and Sochi.
(Reporting by Gabrielle Tétrault-Farber; editing by Ken Ferris)
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