Chara signed a deal with HC Lev Prague of Russia's Kontinental Hockey League, CSN New England reported.
The 35-year-old Slovak defenseman is coming off a 12-goal, 52-point season in which he guided Boston into the seventh game of a first-round playoff exit.
Bergeron, meanwhile, has inked a deal with the Swiss team HS Lugano, joining Boston teammate Tyler Seguin there, the Boston Herald said.
Other Bruins already playing abroad include Dennis Seidenberg (Germany), Andrew Ference (Czech Republic), Tuukka Rask (Czech Republic), Rich Peverley (Finland) and Anton Khudobin (Russia), the newspaper reported.
The lockout Tuesday was on the verge of canceling regular-season game set to begin Oct. 11 after earlier eliminating the NHL's entire pre-season schedule.
"No progress" was made during collective bargaining meetings in New York, NHL Deputy Commissioner Bill Daly said.
Tuesday's negotiating session -- the fourth session in five days -- lasted about 2 hours but produced few results, with no additional meetings scheduled.
Daly said the talks centered on the split of hockey-related revenue.