The Tongan international will leave the Knights immediately, with Storm's general manager of football operations Frank Ponissi pleased to have beefed up his squad ahead of the June 30 deadline.
"An opportunity came up to add some depth to our forward stocks as we come into the important final stage of the season," Ponissi said of the 131-game forward, who has generally been used off the bench.
"We see Richie's signing as a chance to bring some further experience and strength to our roster."
Melbourne will be Fa'aoso's fifth NRL club since debuting in 2004 with Penrith.
He joined the Knights in 2008 where he played 99 games.