Defender Micah Richards made his England debut shortly after Eriksson left the England job in 2006 but played under the Swede when he took charge of Manchester City a year later.
“His man-management was as good as I ever experienced and it meant I could play my best football under him,” Richards, now a pundit on the BBC, said.
“Thank you for everything, Sven.”
Goalkeeper Joe Hart, who did not play for England under Eriksson but became the first-choice goalkeeper under him at Manchester City, said he was “so lovely to be around”.
Hart told the Monday Night Club: “He was just a lovely, lovely man with so much power and so much influence. He just had this beautiful way about him. I was probably too young to appreciate him.”
He added: “This guy cared, this guy had a passionate interest in how we were as human beings.
“He was an absolute superstar everywhere he went and he just owned it, just oozed class and it didn’t look like effort. These are the things I think about when I think of him.”
Former Leicester goalkeeper Kasper Schmeichel said “we have lost an incredible man to whom I owe a great deal”.
Schmeichel was given his Premier League debut by Eriksson at Manchester City and was signed again by the former England boss during his spells at Notts County and Leicester.
Schmeichel would go on to win the Premier League title with Leicester in 2016.
“Sven was the first manager to truly believe in me and give me a chance at the highest level,” Schmeichel said.
“He was the first manager to call me world-class and he made me feel 10 feet tall.
“He gave me my Premier League debut, brought me to Notts County, and finally to Leicester where I enjoyed the best time of my career.
“It is a great loss to football and the world. I want to thank him for everything he did for me.”
Inter Milan manager Simone Inzaghi won the Serie A title under Eriksson with Lazio in 1999-2000.
He said his passing is a “a great pain for me”.
“He was fundamental in my growth as a footballer and as a man,” the Italian said.
“I admired his calm, his education, the great respect he had for everyone. For me he was a source of inspiration.
“Sven was a great man, an example for everyone. He taught us to live while he was dying.”