The 18-year-old forward was Ottawa's third pick (No. 28) in the first round of the 2020 NHL Draft.
Greig scored 60 points (26 goals, 34 assists) and had 83 penalty minutes in 56 games for Brandon of the Western Hockey League last season. He was third on Brandon in goals, assists and points.
His father, Mark Greig, played 125 NHL games with four teams during a 17-season pro career and has been an amateur scout for the Philadelphia Flyers since 2007.
"Ridly plays with an edge in all facets of the game," general manager Pierre Dorion said. "He's a highly competitive center with strong character who is difficult to play against, driven and especially motivated. We're looking forward to monitoring his development."
Greig's signing came
two days after the Senators signed forward Tim Stuetzle
, the No. 3 pick in the draft. Defenseman
Jake Sanderson
, chosen with the No. 5 selection, remains unsigned.