Terms of the deals were not disclosed, but Chalmers' is reported to be a three-year pact worth $12 million, while Jones' is a three-year deal worth $4.5 million.
The third year of Chalmers' deal is a team option.
Chalmers has played his entire three-year career with Miami, averaging 7.9 points, 3.7 assists, 2.3 rebounds and 26.7 minutes through 225 games. He is a 41 percent shooter from the floor with a 35 percent clip from three-point range.
Jones is an eight-year veteran with Indiana, Phoenix, Portland and Miami. In 447 career games with 73 starts, the Miami native averages 6.3 points, 2.3 rebounds and 18.9 minutes a game.