In a statement obtained by PEOPLE on Thursday, Alex said: “Hey, Ed. Love you. See you on the other side. Your brother, Al.”
He also shared a black-and-white throwback photo of the two of them as children.
Eddie and Alex, 67, founded their namesake band in the 1970s. Eddie went on to become known as one of the greatest guitarists of all time, and the band was inducted into the Rock and Roll Hall of Fame in 2007. The band was most recently comprised of Eddie, Alex, Eddie's son Wolf and David Lee Roth.
Eddie's final Instagram post, dating back to May 8, is a birthday shoutout to Alex, which he captioned, "Happy Birthday Al!! Love Ya!!"(Alex, an ordained minister, officiated Eddie's 2009 wedding, when he tied the knot with Janie Liszewski.)
On Wednesday, Janie posted an emotional tribute to her late husband, sharing a peaceful photo of their feet as they relaxed on a sandy beach.
"My husband, my love, my Peep," she began the caption. "My heart and soul have been shattered into a million pieces. I never knew it was possible to cry so many tears or feel such incredible sadness."
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"Our journey together has not always been an easy one but in the end and always we have a connection and love that will always be," continued Janie. "Saying goodbye is the hardest thing I have ever had to do so instead I say so long, I will see you again soon in a place with no pain or sorrow."
"Please watch over Kody and I," she concluded, referring to the pair's dog. "We love you and miss you so very much. Love, your PooPee ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️."
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Eddie's wife Janie, ex-wife Valerie Bertinelli and Wolfgang (whom he shared with Bertinelli) were all at the hospital with him at the time of his death.
In his statement announcing his father's death, Wolfgang, 29, shared his disbelief in losing a parent to cancer.
"I can't believe I'm having to write this, but my father, Edward Lodewijk Van Halen, has lost his long and arduous battle with cancer this morning," Wolf wrote on Instagram and Twitter. "He was the best father I could ever ask for. Every moment I've shared with him on and off stage was a gift."
He ended his tribute, writing: "My heart is broken and I don't think I'll ever fully recover from this loss. I love you so much, Pop."