Wasilewski, a free agent after leaving Belgian champions Anderlecht, had been training with the Foxes and signed a one-year deal with the Sky Bet Championship club on Tuesday.
The Poland international defender, 33, suffered a double fracture of his right leg in August 2009 following a horrific challenge from Standard Liege's Alex Witsel and missed the rest of that season but fought back to fitness and helped Anderlecht win the title in 2012 and 2013.
Pearson said: "For anyone to recover from those sort of setbacks and still be as committed as he is, is testament to his drive.
"He has a strong mentality and personality, you don't have to be in his presence for long to realise how focused he is on being successful.
"It is all right getting the right players technically but you have got to have the right mental qualities as well, and I think he brings the type of mentality that we look for."