The Sun and Daily Mirror tabloids bade Italian coach Capello, who quit on Wednesday following the Football Association's decision to strip John Terry of the captaincy, a cheery "Arryvederci".
"Now give it to cleared Redknapp," said The Sun after the Spurs manager was acquitted, just hours before Capello resigned on one of the most dramatic days in English football history.
The paper hailed Redknapp as "the people's choice and the players' choice to rescue England" after Capello, 65, led the side in a disastrous campaign at the 2010 World Cup in South Africa.
"Good riddance," agreed the Daily Mirror, which reported that Capello would leave with a £1.5 million ($2.4 million, 1.8 million euro) payoff despite abandoning the side before Euro 2012.
Capello's reign was "characterised by a general sense of confusion, apathy, miscommunication and mediocrity", Oliver Holt wrote in the Mirror.
The paper's Mark Lawrenson said Redknapp could bring "a hunger, style and will to win which was missing from the end of Capello's reign".
Capello's position had come under scrutiny after he told an Italian broadcaster on Sunday that he disagreed "absolutely" with the dismissal of Terry, who faces a criminal trial for allegations of racially abusing QPR defender Anton Ferdinand during a Premier League match in October 2011.
Although senior FA officials were known to be unhappy with Capello's comments, the former AC Milan and Real Madrid coach was expected to remain for the final few months of his contract, which would expire after Euro 2012.
However in a bombshell announcement released shortly after 7.20pm (1920 GMT), the FA confirmed that Capello's four-year reign was over.
"The Football Association can confirm that Fabio Capello has today resigned as England Manager," the statement said, following discussions between Capello, FA chairman David Bernstein and FA General Secretary Alex Horne.
Capello was not immediately available for comment. FA officials have scheduled a press conference at Wembley on Thursday.
The Guardian too expressed little regret over the departure of the former AC Milan and Real Madrid coach, who took charge of England in December 2007.
"Fabio Capello never bothered to learn much English, or much about England," wrote Richard Williams.
"His £6 million ($9.5 million, 7.2 million euros) a year was not enough to interest him greatly in the culture of the country whose national game he was hired to revive by winning a major international tournament."
Henry Winter added in the Daily Telegraph that Capello "stamped his feet like a stroppy child" over the decision to axe Terry, who faces a criminal trial over claims he racially abused Queens Park Rangers' Anton Ferdinand.
The Independent agreed: "To quit over the FA taking a stand that it was inappropriate for the England team to be led by a man on a charge of racial abuse is a pathetic waste."
Much of the press paid tribute to Redknapp's human qualities, which were much on show during a two-and-a-half week trial at which he confessed to being "utterly disorganised" and baffled by modern technology.
"In the backlash from Capello's four years of calamity, the London vowels of Redknapp sound like the voice of sweet sanity," Simon Barnes wrote in The Times, declaring Redknapp "made for the job".
The Daily Express said Redknapp, the most successful English manager currently working in football, had "the elusive knack of lifting players and of making them believe in themselves".
"Good luck to Harry Redknapp," concluded Matt Dickinson in The Times."He is going to need it."
One bookmaker immediately suspended betting on Redknapp replacing Capello as odds on the Londoner taking over were slashed.
Former England managers Graham Taylor and Sven-Goran Eriksson both said Redknapp would be a logical successor.
England players meanwhile reacted with shock to news of Capello's departure, with striker Wayne Rooney confessing he was "gutted" by the news.
"Gutted capello has quit. Good guy and top coach. Got to be English to replace him. Harry redknapp for me," Rooney wrote on Twitter.
Liverpool full-back Glen Johnson also took to Twitter to pay tribute.
"Sad news to see Capello step down. Good man and a Good manager. ThanksForEverything," he wrote.