Hamilton and Rosberg had been Mercedes team-mates since 2013, but the friendly relationship they developed when teenage drivers in karting collapsed under the weight of their subsequent world title duels.
Despite their rivalry, Hamilton says both he and the sport as a whole will miss Rosberg.
"It's going to be very, very strange and it will be sad not to have him in the team next year," added Hamilton. "The sport will miss him and I wish him all the best.
"Of course it is a shame that he won't allow me to take it [the title] back or fight to take it back but that is his choice and I respect his decision: go out on top while you can."
Until Rosberg's announcement, Hamilton's long-term future at Mercedes had been under the spotlight following controversy at the Abu Dhabi Grand Prix when he ignored team instructions and deliberately slowed his team-mate in an attempt to make the German lose positions.
Asked who he would like to see alongside him at Mercedes in 2017, an unfazed Hamilton replied: "It doesn't matter who...I'll race them, I'm here to race."