The Nuggets acquire guard Isaiah Whitehead in the trade, whom they will waive, league sources said.
The deal frees $21 million in salary that potentially saves Denver $43 million in payroll and luxury tax in 2018-19.
Nets general manager Sean Marks continues to replenish Brooklyn's arsenal with first-round picks. Denver's 2019 first-round pick is protected 1-12, and the 2020 second-round pick is unprotected.
In 2017, the Nets traded for DeMarre Carroll, whose salary fetched them a 2018 first-round pick.
The Nets were able to absorb Faried's and Arthur's contracts because of the $1.5 million free-agent cap hold of Joe Harris. The trade would not have worked had Brooklyn signed Harris to his $8 million cap hit once the moratorium was lifted.
Brooklyn still has $2.6 million in cap space available, with 14 players under contract. The Nets can exceed the cap to sign Harris because of the early Bird exception. The $4.4 million room midlevel exception is reserved for Ed Davis.
ESPN's Bobby Marks contributed to this report.