The team officially signed the Croatian forward to a three-year deal on Tuesday. The contract is worth $10 million, according to league sources.
The 6-foot-8 forward was drafted 31st overall in 2011 by Miami before having his draft rights dealt to the Nets.
"Having drafted Bojan in 2011, it is rewarding to finally welcome him to the Nets," general manager Billy King said in a team statement. "We obviously have a high regard for his game, and we are glad he will now bring that talent to Brooklyn."
Bogdanovic, 25, spent the last three seasons with Fenerbahçe Ülker in the Turkish Basketball League. He averaged 14.8 points, 2.4 rebounds and 1.9 assists in 30.6 minutes per game during the 2013-14 Euroleague season.
The Nets passed on making an offer to re-sign Paul Pierce earlier this month largely because they felt they wouldn't win a title even if they brought Pierce back. The Nets could have paid Pierce -- who signed a two-year, $11 million deal with the Wizards -- more than any other team.
The Nets have high hopes for both Bogdanovic and Karasev. It remains to be seen what the Nets' starting five will be. But with Pierce gone, Andrei Kirilenko, Mirza Teletovic, Alan Anderson, Bogdanovic and Karasev will try to fill the Pierce void.