The 34-year-old winger, who is out of contract at St Helens at the end of the year, has signed a 12-month deal and will join Adrian Morley (Warrington) and Junior Sa'u (Melbourne) at the Salford City Stadium in 2014.
Meli, who has scored 140 tries from 215 appearances for Saints since joining them from the New Zealand Warriors in 2006, will be a direct replacement for out-of-contract England Knights winger Jodie Broughton, who is thought to have agreed a long-term deal with Huddersfield.
A St Helens spokesman said: "We'd like to place on record our gratitude to Francis for his effort and commitment to the club since he signed in 2006.
"He has been a consummate professional and one of our strongest strike players in the Super League era. We're sure Francis will want to finish his Saints career on a high."
Salford chief executive Ed Farish confirmed the signing of Meli, who won 24 caps for the Kiwis, and added: "I expect there will be another two new faces shortly."
The Reds lost out in attempts to sign Bradford forward Elliott Whitehead, who joined Catalan Dragons instead, and Hull KR scrum-half Michael Dobson, who is returning to Australia.
But they are thought to be close to signing Meli's St Helens team-mate Tony Puletua and remain favourites to land the signature of Castleford's England half-back Rangi Chase.
- Sports & Recreation
- Salford City Stadium
- Adrian Morley
- New Zealand Warriors