England's campaign team said on Thursday that Russian Sports Minister Vitaly Mutko had given its bid an "honourable" apology.
"We of course accepted this apology and appreciate the gesture," the England bid team said in a statement. "We now wish to move on from this matter."
"I'm glad this whole thing is finally over to our mutual satisfaction and we can now proceed with our normal work," Sorokin told Reuters.
Football's governing body FIFA is due to elect the hosts of the two World Cup tournaments on December 2 in Zurich.
COMMENTS "DISTORTED"
He later said his comments had been "misinterpreted and distorted".
Last week, two members of FIFA's executive committee were provisionally suspended on suspicion of selling their votes in the contest to host the two tournaments.
Nigerian Amos Adamu and Tahiti's Reynald Temarii, who have both denied wrongdoing and said they expect to be cleared, were banned from all football-related activity for 30 days while FIFA's ethics committee investigates allegations they offered to sell their votes when approached by undercover journalists.
