The 25-year-old forward was a restricted free agent and avoided a salary arbitration hearing scheduled for Aug. 1.
Joseph had 30 points (12 goals, 18 assists) in 69 games for the Senators and Tampa Bay Lightning last season, including 12 points (four goals, eight assists) in 11 games after he was acquired in a trade with the Lightning on March 20.
"Mathieu's addition made an immediate positive impact as someone who fit in well with our group," Ottawa general manager Pierre Dorion said. "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."
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Selected by Tampa Bay in the fourth round (No. 120) of the 2015 NHL Draft, Joseph has 82 points (41 goals, 41 assists) in 232 regular-season games and two assists in 10 Stanley Cup Playoff games.
Joseph won the Stanley Cup with the Lightning in 2020 and 2021.
