Steven Weber and his girlfriend, Kenesha Antoine, were staying in a submerged cabin at the Manta Resort, off Pemba Island.
Footage shows Mr Weber diving underwater to ask Ms Antoine to marry him.
In the video according to the BBC report, Mr Weber presses a hand-written proposal note against the cabin window as Ms Antoine films from inside.
Ms Antoine, confirming Mr Weber’s death in a Facebook post, said he “never emerged from those depths”.
The Manta Resort told the BBC Mr Weber “tragically drowned while free diving alone outside the underwater room” on Thursday afternoon.
“It is with the deepest regret that we inform that a fatal accident occurred at The Manta Resort on Thursday 19 September 2019,” the resort said in a statement.
Mr Weber and Ms Antoine had booked four nights at the resort’s underwater room, which lies approximately 250m (820ft) from the shore.
Costing $1,700-a-night (£1,300), the cabin is anchored in water around 10m (32ft) deep.
On the third day of their stay, Mr Weber, from Baton Rouge, Louisiana, plunged into the water to make his proposal.
Wearing goggles and flippers, he held a note against the cabin’s glass window as Ms Antoine watched on from within.
His note read: “I can’t hold my breath long enough to tell you everything I love about you. But… everything I love about you, I love more every day!”
Later in the video, Mr Weber turns over the sheet of paper to reveal the proposal, before pulling an engagement ring from his shorts and swimming out of view.
In her Facebook post, Ms Antoine said Mr Weber “never got to hear her answer” to his proposal, which would have been “a million times, yes”.
“We never got to embrace and celebrate the beginning of the rest of our lives together, as the best day of our lives turned into the worst, in the cruellest twist of fate imaginable,” she wrote.
“I will try to take solace in the fact that we enjoyed the most amazing bucket list experiences these past few days, and that we both were so happy and absolutely giddy with excitement in our final moments together.”
The US Department of State said it is aware of the death of a US citizen in Tanzania, in East Africa.
“We offer our sincerest condolences to the family on their loss,” a spokesperson said. “We stand ready to provide all appropriate consular assistance.”
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