Sir Bobby Charlton, one of the players Gregg pulled from the wreckage of the burning plane, was among those who gathered to say farewell to a goalkeeper whose courage in the aftermath of the 1958 disaster is part of club folklore.
Fellow United stars Sir Alex Ferguson and Denis Law also attended the service in Gregg's hometown of Coleraine in Northern Ireland.
"Although his background was firmly rooted in football, we have been amazed by the outpouring of admiration being bestowed on him from the entire sporting community and indeed from all walks of life.
"In his own words, being transferred to Manchester United was like a dream coming true, but if truth be told he would have paid to have played for them, if he had been a rich man.
He was also incredibly proud of his connection to Coleraine and even more so that of Northern Ireland.
"Although hurting deeply as a family it is our hope that this time and the funeral itself can be used as an opportunity for supporters everywhere to celebrate his great life, achievements and associations.
"In closing we would like to express our particular gratitude to all the support being received from local authorities, businesses and those assisting with the logistics of the funeral arrangements".
Gregg is also survived by his sons-in-law David and Keith, daughter-in-law Tina, and sister Elizabeth. He was predeceased by his first wife Mavis and daughter Karen.