The team announced Wednesday that Green will get a three-year contract and Richards a one-year deal.
Green has spent his entire career with Washington, recording 113 goals and 247 assists in 575 games. He is the second-highest scoring defenseman in the NHL over the past eight seasons and will be counted on to quarterback Detroit's power play. Green had 10 goals and 35 assists last season with the Capitals.
Richards comes over from Chicago after winning his second career Stanley Cup. The 35-year-old had 12 goals and 25 assists in 76 games for the Blackhawks last season. He added three goals and 11 assists in the playoffs.