Richards, 46, has led the Blue Jackets to a 42-38-9 record in 99 games, including a 24-17-7 mark and a franchise-best .573 winning percentage in the 2012-13 season.
The club tied for eighth in the Western Conference last season with 55 points, ending their campaign on an impressive 19-5-5 run.
"We believe Todd is one of the top young coaches in our game and he has had a steadying influence on our team since taking over as head coach in January 2012," Columbus general manager Jarmo Kekalainen said.
"The hard work put in by Todd and our coaching staff has been a big reason for our team's improved play and we are excited that he will continue to serve as our head coach."
Richards compiled a 77-71-17 record in two seasons as head coach of the Minnesota Wild before being appointed head coach of the Blue Jackets on a two-year deal in May 2012.
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