The move comes after members of the orchestra failed to agree on who should take the post after an 11-hour meeting in May.
Mr Petrenko, 43, is currently general music director at the Bavarian State Opera in Munich.
He said he felt "great joy" at being elected to the post.
"I am aware of the responsibility and high expectations of me, and I will do everything in my power to be a worthy conductor of this outstanding orchestra," he said.
Orchestra Board members Ulrich Knorzer and Peter Riegelbauer said they were "extremely pleased that Kirill Petrenko has accepted his election as chief conductor designate of our orchestra."
Sir Simon said he had admired Mr Petrenko for many years and was delighted that the Russian was succeeding him.
