Boycott is reported to have said it would be more likely he would be knighted if he was to 'black his face'.
It is also claimed he said some knighthoods were handed out like "confetti" to West Indies greats.
The 76-year-old has now described his comments at a Q&A in Birmingham on Saturday as "clearly wrong".
The Yorkshireman added he loves West Indian cricket and has "the utmost respect for its players".
The Q&A event, hosted by Sky Sports presenter Gary Newbon, was held during a break in play and was attended by about 200 people.
Waheed Saleem, who was in the audience, told BBC Sport: "I was completely disgusted. I don't think anyone saw it as a light-hearted joke. I was absolutely gobsmacked."
Boycott was part of the BBC's Test Match Special commentary team for England's day-night Test against West Indies at Edgbaston last week.
A BBC spokesperson said: "He has rightly apologised unreservedly for these clearly unacceptable comments.
"We use a number of different contributors in our cricket coverage. He remains part of our team."
It is also believed that Boycott will remain part of Channel 5's team for the second Test at Headingley, which starts on Friday.
A spokesperson for Warwickshire County Cricket Club said: "We were very disappointed by Geoffrey's comments and are pleased to see that he has apologised and recognised that it was unacceptable."
Former England cricketer and BBC commentator Geoffrey Boycott has apologised for an "unacceptable" comment about West Indian cricketers.