The US$900,000 contract is for the 2022-23 season.
Brannstrom, 23, hit new career highs in assists (14), points (14) penalty minutes (30) and games (53) with the Senators last season. He also played in nine games for the American Hockey League's Belleville Senators.
“Erik is among our group of young players who we’re looking upon to take another step forward next season,” said Ottawa general manager Pierre Dorion. “He’s competitive, has an ability to efficiently move the puck and showed well when asked to take on an increased role last season.
"We’re hopeful that experience pays dividends for him in the year ahead.”
Brannstrom had a goal and two assists in 10 penalty minutes for Belleville.
A native of Eksjo, Sweden, Brannstrom has two goals and 29 assists with 71 penalty minutes over 116 NHL games, all for Ottawa.
Brannstrom helped Sweden to a silver medal at the 2018 IIHF World Junior Championship in Buffalo, N.Y., with a goal and three assists.
This report by The Canadian Press was first published Sept. 5, 2022.
The Canadian Press