The average annual value is $2.95 million.
The Senators and Joseph were scheduled to go to arbitration on Monday before making the deal.
The Senators acquired Joseph in a trade that sent fellow forward Nick Paul to the Tampa Bay Lightning last season.
Joseph, 25, registered 12 points (four goals, eight assists) over 11 games with the Senators. He concluded the season with NHL career highs in assists (18) and points (30) over 69 contests split between Tampa Bay and Ottawa.
“Mathieu’s addition made an immediate positive impact as someone who fit in well with our group,” said Senators general manager Pierre Dorion. “He has high-end speed, a nose for the net and is responsible in his own end. He’s long demonstrated good upside and is someone we’re counting on to have another solid season both in 2022-23 and beyond.”
The native of Laval, Que. has 41 goals and 41 assists in 232 career NHL games.