The deal was completed on Tuesday, just a day after the Nets handed Morrow an offer sheet on a three-year, $12 million contract.
The Warriors, who were not expected to match the offer, will get the Nets' second-round draft pick in 2011. The pick is protected if it falls between 31 to 55.
Morrow averaged 13.0 points last season, shooting 46 percent from 3-point range.
"We felt that outside shooting was a primary concern during this offseason," Nets president and general manager Rod Thorn said. "Anthony is one of the premier young shooters in the league and we are very pleased to add him to our roster."
Morrow has averaged 11.6 points and 3.4 rebounds in 54 career games over the past two seasons. The Georgia Tech product was not selected in the 2008 draft and later signed with the Warriors as a free agent. He led the NBA in 3-point field goal percentage in 2008-09, becoming the first Warrior and first rookie to lead the NBA in the category.