Pearson, son of Leicester manager Nigel Pearson, Hopper and Smith were all sacked with immediate effect, Leicester said in a statement.
They are seen laughing as they verbally abuse three Thai women while having sex with them in a Bangkok hotel room during club's recent tour of Thailand, according to the Mirror, which obtained a copy of the video.
During the video, which the players allegedly shared with friends back in Britain, one of footballers can be heard calling one of the woman a "slit eye," the newspaper said.
The club decided to terminate their contracts despite an apology from the trio.
"Leicester City Football Club is acutely aware of its position, and that of its players, as a representative of the city of Leicester, the Premier League, the Football Association and the club's supporters," the statement read.
"It is committed to promoting a positive message of community and family values and equality, and to upholding the standards expected of a club with its history, tradition and aspirations."