The Nets have been openly confident in their ability to re-sign Wallace, who opted out of the final year of his contract last month with the intent of staying with the Nets.
No new contracts in the NBA can be officially signed until July 11, but sources told ESPN.com that Wallace -- originally expected to land a three-year deal worth $24 million -- will instead land the four-year deal.
Wallace opted out of the $9.5 million he was originally scheduled to earn in 2012-13 on June 15 to proceed to free agency.
The Nets paid a high price to acquire Wallace from Portland during the season in hopes of upgrading the roster to convince marquee free agent Deron Williams to commit to the team long term, sending the Blazers their top pick in this year's draft with only top-three protection attached. When Brooklyn finished sixth in the May lottery, Portland took control of the pick and drafted Weber State point guard Damian Lillard.
ESPN The Magazine's Chris Broussard contributed to this report.