The 26-year-old had been linked with a move to the 16th-placed reigning premiers before his two-year deal was announced on Wednesday afternoon.
"He has a hardworking approach to his football and we're excited about what he can bring to the Broncos," said Broncos general manager of football Troy Thomson.
Blore is set to reunite with coach Michael Maguire, who handed the second-rower his NRL debut at Wests Tigers in 2020.
He subsequently joined the Storm as part of a swap deal for premiership winner Justin Olam, who was later forced into retirement by injury.
Blore was an effective presence on Melbourne's left edge on arrival in 2024 and played in two consecutive grand final losses with the club.
But after injuries hampered him early in 2026, Blore fell out of favour and has managed only 10 NRL appearances for the Storm so far this year.
He was consigned to NSW Cup in mid-July as Melbourne were fighting for their finals hopes and started at NRL level last week for the first time since May.
"While we're disappointed to see Shawn leave, we understand his decision and wish him, his partner and their family all the best with their move to Brisbane," said Storm football boss Frank Ponissi.
Blore's next move comes amid significant turnover at the Broncos, who farewell forward pack leader Payne Haas and captain Adam Reynolds at season's end.
Gehamat Shibasaki, Grant Anderson and Jesse Arthars are among other first-graders leaving the club.
With Brendan Piakura battling injuries throughout 2026, Brisbane's lack of depth at second row has been exposed.
Journeymen Jack Gosiewski and Jaiyden Hunt have both earned starting berths throughout the year, but Blore's arrival bolsters the ranks.
Blore has played 91 NRL games and made two international appearances for Samoa in 2024.
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