"Ole and Alexander are talented, young players who showed great improvement over the course of last season and became very difficult to play against," Blue Jackets general manager Scott Howson said.
Tollefsen, a 23-year-old player from Norway who was Columbus' third pick in the 2002 draft, had two goals and three assists in 70 games with the Blue Jackets in his first full season with the team.
The 24-year-old Svitov had seven goals and 11 assists in 76 games, setting career highs in goals, assists, points, penalty minutes and games. The Russian was acquired from Tampa Bay in a trade for defenceman Darryl Sydor.
Brookbank, 26, signed a one-year contract after scoring 15 goals and adding 38 assists in 78 games with Milwaukee of the AHL last season. He played three games with the Predators last season, picking up his only NHL point with an assist against Pittsburgh on Feb. 6.