The Football Association of Ireland says former manager Jack Charlton “changed Irish football forever”.
The former Leeds and England defender, who had been diagnosed with lymphoma, died on Friday aged 85.
England said it was “devastated” by the death of a key member of the 1966 World Cup-winning side.
Tributes were also paid by former clubs Leeds, Newcastle, Sheffield Wednesday and Middlesbrough.
Charlton spent his entire playing career with Leeds between 1953 and 1973, before joining Middlesbrough later that year in his first managerial post.
In 1977, he took over at Wednesday and had a spell with his boyhood club Newcastle before moving into international management with the Republic of Ireland in 1986.
“Charlton’s contribution to the game and Leeds United will never be forgotten,” said the West Yorkshire club.
“He will remain in football folklore forever and his records at Leeds United are unlikely ever to be surpassed.”
Newcastle United said: “We are deeply saddened to learn of the passing of former NUFC manager and England World Cup winner Jack Charlton at the age of 85. RIP, Jack. A true legend of the game.”
Sheffield Wednesday and Middlesbrough said they were “saddened” to hear of Charlton’s death.
One of English football’s most popular characters, he was in the team that won the World Cup at Wembley in 1966, alongside his brother Bobby.
Charlton achieved unprecedented success with the Republic of Ireland, leading them to their first major finals at Euro 88 and the World Cup quarter-finals at Italia 90.
Former Republic of Ireland international John Aldridge, who famously had to be calmed down by Charlton on the touchline at the 1994 World Cup, said he was “absolutely gutted”.
“What a football man, loved and adored, especially in Ireland,” tweeted the former Liverpool striker.
“The best manager I was lucky to play for. The times we had on and off the pitch was priceless. My thoughts are with [Jack’s wife] Pat and the family! RIP my good friend. Never forgotten.”
‘Sad day as Leeds loses another legend’
Ashington-born Charlton never played for his boyhood club Newcastle, instead joining Leeds United as a 15-year-old and spent his whole playing career with the Whites.
Charlton made a record 773 appearances between 1953 and 1973, winning an English league title, FA Cup, League Cup and two Fairs Cups.
He is the third Leeds United legend to have died this year, following the deaths of team-mates Norman Hunter and Trevor Cherry.
The Leeds United Supporters’ Trust hoped the club, which leads the Championship, can seal promotion to the Premier League as a fitting tribute to the three men.
“Another massively sad day for the fans and club as we lose another legend. RIP Big Jack,” it said.
“If there was ever a more prominent year for us to go up it’s now, let’s do it for Jack, Norman and Trevor.”
Current Leeds United captain Liam Cooper said Charlton’s death was “a very sad day”.
‘Epitome of the word legend’
England record goalscorer Wayne Rooney: “Sad news, legend. Condolences to Sir Bobby and family.”
Former England striker Gary Lineker: “Saddened to hear that Jack Charlton has passed away. World Cup winner with England, manager of probably the best ever Ireland side and a wonderfully infectious personality to boot.”
Former Republic of Ireland defender Paul McGrath: “Absolutely gutted. Father figure to me for 10 years, thanks for having faith in me. Sleep well Jack, Love ya. Broken heart.”
Times football writer Henry Winter: “Sad, sad day. RIP Jack Charlton. Epitome of the word legend. A winner as a player, gave everything for Leeds United and England. Inspirational manager and wonderful company. He lived the fullest of lives and enriched so many lives. Thoughts with Jack’s family and his many, many friends.”
Independent football writer Miguel Delaney: “Jack Charlton was the biggest football figure of my youth, and no doubt the same for two generations of Irish people.”
Football Focus presenter Dan Walker: “How sad to hear. One of England’s World Cup winners & legendary Republic of Ireland boss. We’ll do our best to pay tribute to Big Jack on Football Focus.”