IBF, WBA and IBO heavyweight champion Joshua knocked out veteran Klitschko in the 11th round in an epic Wembley bout in April.
It had been expected that Klitschko, whose nine-year reign as lineal world heavyweight champion was ended by Tyson Fury in 2015, would agree to a rematch with Joshua in Las Vegas.
However, the 41-year-old instead decided to hang up his gloves, a decision the unbeaten Joshua said he saw coming.
"In my heart of hearts I kind of knew he probably wouldn't fight again," he said.
