The Devils did not tender offers to forward John Hayden and defenseman Mirco Mueller, who has been part of their back line for three seasons.
All seven players were restricted free agents.
The 23-year-old Blackwood emerged as the Devils' top goaltender last season, posting a 22-14-8 record with a 2.77 goals-against average and three shutouts. New Jersey missed the playoffs with a 28-29-12 record.
Bratt, 22, has spent the past three seasons with the Devils. He had 16 goals and 16 assists this past season and has 37 goals and 63 assists in his career.
Anderson had four goals in 18 games this past season. White played in six games and Merkley, who was acquired in the deal that sent Taylor Hall to Arizona, played in four.
Mueller, a 25-year-old Swiss player who was acquired from San Jose in 2017, appeared in 50 games this past season with two goals and five assists. Hayden played in 43 with three goals, an assist and 77 penalty minutes.
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