The entrepreneur and star of BBC's The Apprentice tweeted that one of his Twitter "racial abusers" was convicted at Chelmsford Magistrates' Court.
He added that the "level of abuse was so great I had to ask for help".
The court said the 17-year-old, from Preston, Lancashire, admitted sending racially aggravated communication and was handed an eight-month referral to a youth offender panel.
He was also told to pay £85 costs, a £15 victim surcharge and £100 compensation to Lord Sugar at the hearing on Wednesday.
In a series of tweets, Lord Sugar, who lives in Chigwell, thanked Essex Police for "tracking him down".
Responding to a follower who said "surely the police have better things to do", he said: "They do but the level of abuse was so great I had to ask for help and am truly grateful something had to be done."
Lord Sugar himself was investigated by Merseyside Police in 2013 after being accused of posting a racist message on Twitter, but it said "no criminal offences" had taken place.
A youth has been told to pay Lord Sugar £100 for racist abuse on Twitter.