The fly-half, 23, will start against Ulster at Scotstoun on Friday evening, following the compulsory graduated return-to-play protocol.
It is a key game for the Warriors, who sit two places outside the Pro12 play-off positions
"I was desperate to pass all my tests and get back into it," Russell said.
"For the other [international] boys coming back, it's such a big six games for us that if we slip up one game, that could be our season over almost.
"So, the pressure is on us. That's good for the boys coming back."
Russell was concussed during Scotland's 29-18 victory over France and missed the final Six Nations match against Ireland and Glasgow's victory over Leinster last Friday.
Ulster are one place ahead of Gregor Townsend's reigning champions in the table, with both sides still hopeful of reaching the play-offs.
As the Warriors try to become the first team to retain the Pro12 title, Russell feels the return of international players is timely.
"This year's different from last year, when we were top of the league at this point," he explained.
"If we lose one or two of the next six games then we're relying on other teams to lose, which we don't want to do. We're still in the mix, we've still got six games left and one in hand, it's still in our hands.
"It was a tough year, especially after winning last year and having the World Cup taking a lot of us away [at the start of the Pro12 season].
"It's been a transition year almost, but looking at the boys as they beat Leinster last weekend, the way they played was amazing, and it gives us coming back from the Six Nations a bit more energy.
"We know we've got to play for our positions now. We are getting back to our best. There's still a lot to work on, but we're getting back on form where we need to be if we're to do the same as last year.
"The boys coming back from a good Six Nations can try to bring a bit more leadership, things that we learned.
"It's just getting back to how Glasgow play - that's slightly different to Scotland - and getting used to what it's like here as quickly as possible. It does help that with Scotland there are a lot of Glasgow boys there, but the quicker that we can get back into the Glasgow routine, the better."
Finn Russell has been "desperate" to return to action with Glasgow Warriors after suffering concussion during Scotland's Six Nations campaign.