The 47-year-old is the second Premier League manager to test positive for the virus after Arsenal's Mikel Arteta.
Rodgers started displaying symptoms soon after Leicester's 4-0 win over Aston Villa on March 9 - the final match before top-flight football was suspended because of the pandemic.
Both he and his wife have made a full recovery, with Rodgers taking training as the Foxes prepare for the Premier League's prospective June 17 return.
"We spent about three weeks, both of us, feeling the effects of it. We were nowhere near as bad as many others but we lost our smell and taste and our strength," said Rodgers.
"I had a little feeling of what it was like, it was tough. Once we got back fit and well it made us really appreciate our health and I've taken the opportunity to get back to being as fit as I can be.
"The strangest thing was losing your smell and the taste, you lose your strength, you could hardly walk 10 yards. I felt it was similar to the time I was climbing Kilimanjaro. When you get to a certain point at altitude you walk and really suffer.
"The first time I tried to exercise I couldn't run 10 yards. It really does knock you but it wasn't as serious as a lot of people have had. You come out of it grateful you are fine."
