The pair will join the English club immediately after playing a combined 12 games for Gold Coast this season.
Back-rower Stone is the son of former Huddersfield and Newcastle coach Rick Stone. The 23-year-old began his career at Newcastle in 2017 before moving to the Titans where he has played just 21 matches over three seasons.
Speaking to the club after the deal, which runs to November 2022, was announced, Stone expressed his appreciation for the English game style.
"I've always wanted to play in England, and I think the style of footy will be great for me," Stone said.
"The game in the NRL is very conservative and the English game is much more open and as a player you have the opportunity to express yourself.
“My dad said I should go for it, and he encouraged me to sign. After I had spoken to the owner and the coach at Leigh, I was excited after hearing of their enthusiasm and their plans for the future."
Stone's teammate, prop Whitbread, debuted for the Titans in 2018. The 23-year-old has since gone on to play 30 games, managing just two under Justin Holbrook this season.
— Leigh Centurions (@LeighCenturions) August 2, 2021
The son of former Canterbury and Gold Coast Giants player Greg Whitbread, Jai grew up playing in Queensland where he represented the Broncos' under 20s side.
“I started playing when I was about seven and my dad played for a few clubs over here (in Australia) and I loved the game." Whitbread said.
"I think I've been playing some good footy here and I'm looking forward to adapting my game and getting used to Super League - it's a tough competition."