Boenisch joined Leverkusen as a free agent at the start of November, initially on a short-term contract until the end of the season.
He was brought in to provide cover for the injured Michal Kadlec and Daniel Schwaab, and settled in quickly.
"It was impressive how quickly Sebastian reached such a significant level after so long without match practice," general manager Wolfgang Holzhauser said.
"He helped us out in a difficult situation and earned everybody's respect in the process."
Boenisch has also earned a recall to the Poland squad during his time with Leverkusen and is now a key figure for the Bundesliga club.
"I am really delighted that I have been able to convince the bosses of Bayer Leverkusen of my quality," the 26-year-old said. "I am very happy in Leverkusen and I would like to support the club in achieving their objectives in the coming years."