The Williams driver finished just ahead of teammate Valtteri Bottas to secure his first pole since the 2008 Brazilian Grand Prix.
The 33-year-old told reporters: "I am so happy with what has happened today, with us, our team, it was such a great moment. It is a long time since I last had a pole position so for sure we need to concentrate on the race tomorrow.
"It is a great moment and I am in the best place to be, first place. After a long time, I hope this is just the beginning of great possibilities. I hope to be in this position again.
"Williams are back to the top, they are back to fight. I am pleased for me and the team as well."
The race is being held at the Red Bull Ring in Austria for the first time since 2003.