Liam Miller was an "unassuming man off the pitch but a brilliant player on it," Celtic legend Pat Bonner said.
The ex-Celtic, Manchester United and Republic of Ireland player, 36, died on Friday after suffering from cancer.
Celtic held a minute's silence in tribute to their former midfielder before the Scottish Cup game against Partick Thistle on Saturday.
"He had amazing ability as a player, but also he was a great, great lad," former team-mate Kevin Kilbane added.
Miller started out at Celtic in 2000 before spells at Manchester United, Leeds, Sunderland, QPR and Hibernian.
He also played for three Australian clubs and hometown side Cork City prior to ending his career in the United States in 2016.
Sunderland will wear black armbands in memory of Miller during their Championship game away at Bristol City on Saturday, and Manchester United players will do the same during Sunday's Premier League game at Newcastle United.
Leeds wore black armbands in their match away at Sheffield United in the Championship's early kick-off on Saturday.
"When we got word he was suffering with cancer a few months ago, it was devastating news, for anyone that played with him," Kilbane, who played with Miller for Republic of Ireland, said on Football Focus.
"And, of course, when the news filtered through last night it was terribly sad, and especially when you think of his wife and three children.
"Today, our thoughts just go out to his wife and family."
'He was an excellent footballer and a fantastic man'
Republic of Ireland boss Martin O'Neill gave Miller his debut during his time as Celtic manager where he rose to prominence particularly through his performances in Europe.
"I remember the impact that Liam had in a big Champions League match against Lyon," said the Northern Irishman.
"We were pressing strongly and trying to find the breakthrough when Liam scored a magical goal that gave us momentum to win the game.
"At the end of that season, Liam moved on to Manchester United but had already made a strong mark at Celtic Park and the players were extremely disappointed to see him go.
"Liam's passing is very sad and he will be greatly missed. He was an excellent footballer and a fantastic man."
Many of Miller's former clubs and team-mates have expressed their sadness, including former Celtic team-mate Stiliyan Petrov.
Petrov, 38 and now retired, returned to football in 2016 having recovered from acute leukaemia, four years after being diagnosed with the disease.
He said he was "deeply saddened to hear of the passing of my friend and old team-mate Liam Miller".
Former Celtic and Republic of Ireland goalkeeper Bonner told BBC Scotland: "We will remember Liam and those goals he scored, especially in Europe.
"He was an unassuming young man off the pitch but he was a brilliant player on it."
Brian McClair was a striker at Celtic and Manchester United and said: "At Manchester United, Liam Miller was a quiet, unassuming, humble lad who loved playing and training - always striving to give his all everyday.
"A model pro. Condolences to his family and friends."