Stone, a 2015 Calder Trophy finalist, agreed to a three-year contract with an average annual value of $3.5 million. Zibanejad agreed to a two-year contract with an average annual value of $2.625 million.
Stone, 23, led the Senators with 26 goals and was second to defenseman Erik Karlsson with 64 points.
"Mark became one of our better players, if not one of the best, right at the end of the year in particular, but throughout the stretch run and when we were trying to make the playoffs," general manager Bryan Murray said. "We feel he still has growth in him but we also know going forward that he's going to be a very important player if the organization is going to make strides to a championship."