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."
Alexei Sorokin, director of the Russian bid and the man whose quoted comments in a Russian newspaper sparked the row, said he was happy to see a line drawn under the issue.
"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.
England and Russia are two of four candidates for the right to stage the 2018 World Cup, with joint-bids from Spain/Portugal and Belgium/Netherlands the other hopefuls. Japan, South Korea, Australia, United States and Qatar are candidates for 2022.
Football's governing body FIFA is due to elect the hosts of the two World Cup tournaments on December 2 in Zurich.
The row between Russia and England only added to the problems surrounding the bidding process, which has been rocked by allegations of corruption.
COMMENTS "DISTORTED"
FIFA forbids competing nations from making any comments about rival bidders.
Sorokin was quoted as telling the Sport-Express daily newspaper that London had the highest crime rate compared with other European cities and the highest level of alcohol consumption among young people.
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.
FIFA is also investigating claims of collusion and vote-swapping between unnamed bidders for the 2018 and 2022 bids, which is banned by the rules.
