Philadelphia received a fourth-round pick in the 2023 NHL Draft in return for the center. The Flyers will retain 50 percent of Brassard's salary.
Brassard can be an unrestricted free agent at the end of the season. He has scored 16 points (six goals, 10 assists) in 31 games this season.
"Brassard can play left wing, he can play center," Oilers general manager Ken Holland said. "He's had a good playoff resume and gives us more depth as we push to try and qualify for a playoff spot."
The Oilers (35-23-5) are third in the Pacific Division, three points ahead of the Vegas Golden Knights.
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Selected in the first round (No. 6) of the 2006 NHL Draft, Brassard has scored 519 points (200 goals, 319 assists) in 936 regular-season games for the Columbus Blue Jackets, New York Rangers, Ottawa Senators, Pittsburgh Penguins, Florida Panthers, Colorado Avalanche, New York Islanders, Arizona Coyotes and Flyers. He has scored 68 points (25 goals, 43 assists) in 117 Stanley Cup Playoff games.
The 34-year-old scored his 200th NHL goal in a 3-1 loss to the Carolina Hurricanes on March 12.
The Oilers acquired defenseman Brett Kulak in a trade with the Montreal Canadiens on Monday for defenseman William Lagesson, a conditional second-round pick in the 2022 NHL Draft and a seventh-round pick in the 2024 NHL Draft.
Philadelphia (20-31-11) is seventh in the Metropolitan Division.