The 33-year-old was a free agent, which has allowed him to move outside the transfer window, and he has agreed an initial one-year deal at the King Power Stadium.
Wasilewski, who has over 60 caps for Poland, left Anderlecht in the summer after a six-year spell with the Belgian giants.
"I'm really pleased to be joining Leicester City. I have always dreamed of playing in England so to sign for Leicester is fantastic for me," he told Leicester's website.
"I saw the team beat Wigan at the weekend and was very impressed with everything about the club. It has been a very good start to the season and I hope to be able to help us win promotion to the Premier League."
Wasilewski is not available to face Blackburn on Tuesday, but he could feature in their trip to Blackpool at the weekend.