Eriksson, the first non-British manager of the England team, led the Three Lions to the quarter-finals at three major tournaments during his five-year spell in charge between 2001 and 2006.
In January Eriksson said he had "at best" a year to live after being diagnosed with cancer.
His children, Lina and Johan, said on Monday: "Our father Sven-Goran Eriksson fell asleep peacefully in his home at Bjorkefors outside Sunne this morning. He has for a long time fought bravely with his illness, but now it came to an end.
"Dad told us at the beginning of this year about his serious illness and received an amazing response from friends and football fans around Europe.
"He was invited to several football teams in England, Italy, Portugal and Sweden. They shared their love for football and for dad.
"It was unforgettable for both him and us. He expressed his appreciation and joy and stated that such beautiful words are usually only uttered when someone has died.
"We hope that you will remember Svennis as the good and positive person he always was both in public and at home with us."
Sven Goran Eriksson visited many of his former clubs this year, including Lazio in May
The Swede managed 12 clubs, including Manchester City, Leicester, Roma and Lazio, winning 18 trophies.
Eriksson also had spells in charge of Mexico, Ivory Coast and the Philippines.
After retiring as a player at the age of 27, Eriksson began his managerial career with Degerfors in 1977 before joining fellow Swedish side Gothenburg, where he won the Swedish title, two Swedish cups and the 1982 Uefa Cup.
He then went on to enjoy two spells with Portuguese giants Benfica as well as managing Italian sides Roma, Fiorentina, Sampdoria and Lazio - where he won seven trophies including the Serie A title, two Italian Cups and the European Cup Winners' Cup.
Following his diagnosis Eriksson spent the year visiting some of his former clubs, including Lazio and Sampdoria.
In March the Swede, a lifelong Liverpool fan, helped lead a Liverpool Legends team which beat an Ajax Legends side 4-2 at Anfield.
He shared a poignant message at the end of his new documentary film 'Sven', which was released earlier this month.
He said: "I hope you will remember me as a positive guy trying to do everything he could do.
"Don't be sorry, smile. Thank you for everything, coaches, players, the crowds, it's been fantastic. Take care of yourself and take care of your life. And live it."
One of Eriksson's most famous results as England boss was a 5-1 win over Germany in Munich to help the Three Lions qualify for the 2022 World Cup
Eriksson resigned as Lazio manager in January 2001 to succeed Kevin Keegan as England boss.
He revived a flagging 2002 World Cup qualifying campaign to secure their place at the tournament in Japan and South Korea, including a stunning 5-1 victory over Germany in Munich.
The Three Lions defeated Argentina 1-0 in the group stage at that tournament but were beaten 2-1 by eventual winners Brazil in the quarter-finals. They would also reach the last eight two years later at Euro 2004, before losing to hosts Portugal on penalties.
In January 2006, after securing England's place at that summer's World Cup, it was announced that Eriksson was to leave following the tournament in Germany despite having two years left on his contract.
No official reason was given for his departure at the time, although the Swede had come under pressure after being caught in a newspaper sting by a tabloid journalist.
England went on to reach the quarter-finals again but were beaten once more by Portugal on penalties.
Eriksson's years as England manager were marked by scandal over his private life, including newspapers revealing affairs with television presenter Ulrika Jonsson in 2002 and former Football Association secretary Faria Alam in 2004.
Eriksson went on to have a nomadic career following his England departure, including leading Manchester City to ninth in the Premier League during the 2007-08 season.
He also had a short spell as director of football at League Two side Notts County in 2009-10 and 18 months in charge of Leicester, then in the Championship, between 2010 and 2011.
His final club jobs were with Chinese Super League sides Guangzhou R&F, Shanghai SIPG and Shenzhen between 2013 and 2017.
On the international front Eriksson failed to lead Mexico to the 2010 World Cup, although he would go to the tournament in South Africa as coach of the Ivory Coast, where they failed make it out of their group.
His final managerial position was a 10-game spell as Philippines boss between October 2018 and January 2019.
'A true gentleman of the game'
The Prince of Wales, who is president of the Football Association, was among those to pay tribute to Eriksson.
"Sad to hear about the passing of Sven-Goran Eriksson," he said.
"I met him several times as England manager and was always struck by his charisma and passion for the game. My thoughts are with his family and friends. A true gentleman of the game."
FA chief executive Mark Bullingham said: "This is a very sad day. He gave all England fans such special memories. No one can ever forget the 5-1 victory in Munich against Germany under Sven's guidance.
"Sven will be rightly recognised and forever remembered for his significant work with the England team, and for his wider contribution to the game."
Prime Minister Sir Keir Starmer said: "Deeply saddened to hear that Sven-Goran Eriksson has passed away.
"He will be remembered for his tremendous contribution to English football which brought joy to so many over the years. Our thoughts are with his family."