Blatche and Livingston had previously agreed to terms, but the transactions could not be announced until Wednesday at the earliest because of the NBA's annual moratorium on signings and trades.
Terms were not disclosed Thursday. According to sources, Blatche will get a two-year contract worth approximately $2.9 million overall with a player option for the second year, and Livingston will get a one-year contract worth the veteran's minimum.
"Andray was a vital member of our team last season," Nets GM Billy King said in a statement. "He provides valuable frontcourt depth, and we look forward to his continued contribution.
"Shaun's abilities give our roster added versatility in the backcourt. His basketball acumen and the way he plays the game are a great fit for this team.”
The Nets and Celtics have to wait until Friday because forward Kris Joseph can't be traded until exactly three months have elapsed from the day he signed with Brooklyn as a free agent.