"Mighty's on the other side now," the 47-year-old wrote.
"After seven days of searching from sunrise to sunset and into the wee hours, today, the 7th day we found his collar.
"I have wept more this week than I thought possible, which has been very cathartic and healing."
Bloom, who is expecting a baby with pregnant fiancee Katy Perry, went on to say he "left no stone unturned" in the hunt for his missing dog, before finally realising his tragic end.
"I crawled thru all the manholes, under the roads, searched every backyard and creek bed," he said, adding they even had "two separate sniffer dogs" on the job as well.
After finding the collar that proved Mighty had died, Bloom described feeling "grateful" for his four-legged friend.
"I feel so grateful to have learned from my little Mighty man that love is eternal and the true meaning of devotion," he said in the tear-jerker post.
He explained that Mighty was "more than a companion", calling him a "soul connection" and shared a series of photographs of them together as well as his new tattoo.
The inking, which is on Bloom's left pec, reads: "MIGHTY."
It also features an elaborate love heart symbol underneath.
Bloom signed off the post by thanking neighbours for allowing him to "search through their yards" and for "supporting my midnight walks" in the hunt for his dog.
His raw grief has touched the Lord Of The Rings actor's 4.1 million followers, who have flooded his post with condolences.
Actress Jennifer Aniston – who reportedly had joined in the search for Mighty – said she couldn't stop crying.
"The tears won't stop," she wrote. "I'm so so so deeply sorry my friend. I love you."
Another friend wrote: "Gutted and heartbroken. I'm so so sorry. What a sweet baby he was. I hate it. Sending so much love. I cannot imagine the pain."
While Stranger Things star Millie Bobby Brown said: "I'm so sorry! I understand that feeling and it's honestly the worst. I'm sending my love to you and your family right now."
Previously, Bloom had described Mighty going missing as "a waking nightmare" and pleaded for people to be on the lookout for his "little man".
The dog went missing on July 15 in Montecito, California.