Palmer, a seven-time major winner, died aged 87 in Pittsburgh on September 25 due to complications of heart problems.
Following a private family funeral, a public memorial service was held in his home town, which was attended by leading players past and present from around the world.
The congregation at Saint Vincent College included many of the victorious American Ryder Cup team including Phil Mickelson, Rickie Fowler and Bubba Watson, as well as former greats Lee Trevino, Tom Watson and Britain’s Nick Faldo.
Former LPGA Tour commissioner Charlie Meacham, also a longtime friend to Palmer, opened the address, followed by current PGA Tour commissioner Tim Finchem, and Palmer’s grandson Sam Saunders, himself a professional golfer.
President of International Golf Federation Peter Dawson, former chief executive of The R&A, and American sports broadcaster Jim Nantz also took to the lectern.
Country singer Vince Gill, meanwhile, paid his own tribute with an acoustic performance and former leading women’s golfer Annika Sorenstam spoke of her memories of a man who did so much great work off the course as he had on it.
Nicklaus recalled their first PGA Tour event together in 1962 at the Phoenix Open, where Palmer had beaten him by 12 shots but encouraged the then up-and-coming golfer on his way to a second place at the start of what would be a long friendship as well as great sporting contests.
The 76-year-old 18-time Major winner said: “Arnold came along when golf needed him most. When TV first embraced the sport of golf, it had a swashbuckling hero in Arnold as the game’s face.
“He was the everyday man’s hero, and played a game we could all appreciate and appealed to everyone.
“If there was ever a problem, I knew Arnold had my back and I had his... I may have had to battle ‘Arnold’s Army’ early on, but I never had to battle Arnold Palmer... He was ‘The King’ of our sport, and he always will be.”
Closing his speech, and fighting back tears, Nicklaus said: “Today I hurt just like you hurt. You don’t lose a friend of almost 60 years and not feel an enormous loss, but my wife often says ‘memories are the cushions of life’.
“Each of you sitting here today, or perhaps at home, has at least one wonderful memory of Arnold Palmer to balance out your hurting heart.... so for today and many years from now, I simply ask you to just remember when... Arnold Palmer touched your life, touched your heart and please, don’t forget why.”
Palmer won 62 titles on the USPGA Tour, including four green jackets at the US Masters, in each even-numbered year from 1958 to 1964, two Open Championships and the US Open in 1960.
Earlier, Saunders had given an insight to Palmer’s persona away from the golf course.
The 29-year-old from Colorado said: “There wasn’t a difference between the man you saw on TV and the man we knew at home. He was so special.
“He was always there for me and for my entire family, he would always take my phone call.
“One of the biggest lessons my grandfather taught me that I will carry with me for the rest of my life is to talk less and listen more.”
Palmer is survived by his second wife, Kit, daughters Amy Saunders and Peggy Wears and six grandchildren.