Howard had made the claim in his autobiography, but Friedel, 43, denied the allegation, saying "it is complete garbage" and demanded an apology.
Howard, 35, said: "I have decided to take Brad at his word.
"I have directed my publisher to amend future copies of my book by striking reference to Brad's opposition."
Friedel tweeted in response: "Glad it's over, happy to move on."
Howard completed a £2.5m move from Major League Soccer side New York/New Jersey Metrostars to United 11 years ago, but needed a work permit.
In his book The Keeper, Howard said Friedel, then playing for Blackburn Rovers, refused to endorse his application with a letter of support.
"The legal team at Manchester United told me that Brad hadn't merely refused to sign a statement on my behalf, he had actively tried to block my transfer," Howard wrote in the book.
"He'd written to the appeals committee suggesting that I shouldn't be given a work permit at all."
Friedel, who remains contracted to Tottenham but is yet to make a first-team appearance this season, said that he was asked to sign a letter of support by then US coach Bruce Arena, but did not because he felt it was inaccurate.
And Howard now concedes: "Brad takes issue with my characterisation of his position and events.
"At the time, I was surprised that Brad would not automatically sign my letter of recommendation and I took this as an opposition to my application.
"Brad later explained that he had not in fact opposed my efforts to seek a work permit, either by writing to the Professional Footballers' Association or otherwise."
Friedel played for the US between 1992 and 2005, while Howard has played for the national team since 2002.
Everton goalkeeper Tim Howard says he now accepts former United States team-mate Brad Friedel did not block his move to Manchester United in 2003.