Hagman succumbed to complications from cancer over the weekend, surrounded by family and friends including Dallas co-stars Patrick Duffy and Linda Gray.
The actor's breakthrough role was as Captain Tony Nelson opposite Eden on the classic 1960s sitcom I Dream of Jeannie from 1965 to 1970.
Eden has opened up about her long friendship with Hagman in a statement posted on her official Facebook account.
"As I received the news this evening and as you read this I still cannot completely express the shock and impact from the news that Larry Hagman has passed," she wrote. "I can still remember, that first day on Zuma Beach with him, in the frigid cold. From that day for five more years, Larry was the centre of so many fun, wild, shocking… and in retrospect, memorable moments that will remain in my heart forever. "
The actress continued: "He was such a key element in my life for so long and even, years after I Dream of Jeannie; our paths crossed many times. Throughout various productions I had the pleasure of watching the Texas Tornado that was Larry Hagman. Amidst a whirlwind of big laughs, big smiles and unrestrained personality Larry was always, simply Larry.
"You couldn't fault him for it, it was just who he was. I am so thankful that this past year I was able to spend time with him and experience yet again 'Larry' in all his Big Texas bravado."
Eden went on to admit that Hagman's death from cancer came as a total shock, given that he'd publicly played down the seriousness of the illness.
She wrote: "I, like many others believed he had beat Cancer and yet we are reminded that life is never guaranteed. My deepest condolences go out to his wife Maj, his son and daughter and his grandchildren, as well as his friends in this time of his passing.
"I can honestly say that we've lost not just a great actor, not just a television icon, but an element of pure Americana. Goodbye Larry, there was no one like you before and there will never be anyone like you again."
Hagman's Dallas co-star Duffy called the star "one of the greatest friends ever to grace [his] life" in his own written tribute.
"The loneliness is only what is difficult, as Larry's peace and comfort is always what is important to me, now as when he was here," Dempsey commented.
Hagman is survived by his wife Maj Axelsson and their adult children Heidi and Preston.
> Larry Hagman's career: Dallas, I Dream Of Jeannie - video
Photo Gallery - Larry Hagman 1931 - 2012: