Bromwich, who has also captained New Zealand, will join the Dolphins on a two-year deal from their inaugural season in 2023.
The prop will turn 35 halfway through the final year of his contract.
Bromwich has played all of 272 NRL games at the Storm and will be a huge chance of becoming the Dolphins first captain.
The Kiwi is the fifth player to join the Dolphins since they were announced as the NRL’s 17th team last October.
Bromwich will join Storm teammate Felise Kaufusi, Eels forward Ray Stone, Broncos flyer Jamayne Isaako and young gun Valynce Te Whare.
The Dolphins have missed out on signing several stars in recent months, including Brandon Smith, Reed Mahoney, Apisai Koroisau, Tino Fa’asuamaleaui, Patrick Carrigan and Christian Welch.
“In building a squad from scratch, we have always been focussed on ensuring we add some real experience to the group we will assemble for the 2023 NRL season,” Dolphins chief executive Terry Reader said.
“Jesse will bring a host of good qualities to the Dolphins’ inaugural roster, not the least of which will be his exposure at the highest levels of rugby league.
“He has been one of the shining lights of the strong Storm system for the last decade so will bring a tremendous level of professionalism with him.
“Jesse has been a part of three NRL grand final victories and has played 29 Tests for New Zealand, so we know he is a winner.
“He comes from a club that has always been big on creating standards and this will be a new and exciting opportunity for Jesse to create and set a standard for future Dolphins players.”
Story first published on Fox Sports Australia