The 32-year-old Malaysian, twice an Olympic silver medallist, had been under a provisional suspension since November after testing positive for anti-inflammatory drug dexamethasone during the world championships three months earlier.
Lee, the winner of 55 titles around the world, had his case heard by a three-member panel in Amsterdam on April 11 and faced a two-year ban which would have all but ended his career but the Kuala Lumpur-based BWF opted for a softer sentence.
Lee will be eligible to compete again on Friday.
"The panel is convinced this is not a case of doping with intent to cheat," the world governing body said in a statement.
However, the panel found that Lee had been "negligent", but ruled that the degree of negligence was "rather light".
Lee's inactivity -- his last match was a defeat to China's Chen Long in the world championship final -- has seen his   ranking slump to 30th in the world.
The qualifying period for the Rio de Janeiro Games begins on May 4 and will run for a year.
Lee, one of Malaysia's favourite sporting sons, remains his country's top ranked shuttler and was nominated last week for Malaysia's 2014 sportsman of the year award.