Richardson, who spent three seasons as an assistant at the NHL level, led the Binghamton Senators to a fourth-place finish in the Eastern Conference last year. Binghamton went 44-24-1-7 before being swept out of the playoffs in the first round.
The 44-year-old jumped almost immediately from his career as a defenceman to life in coaching. He played 1,417 games over 20 seasons before retiring in November 2008.
Assistants Steve Stirling and Matt Meacham also received one-year extensions.