The third year of the contract will reportedly be a player option.
Dinwiddie could have agreed to a four-year, $47-million deal, but the 25 year old opted to enter free agency earlier.
Reported annual contract details
The deal comes a day after the combo guard scored a career-high 39 points in a 127-124 win over the Philadelphia 76ers.
Dinwiddie has shown improvement since joining the Nets in 2016. He's currently averaging 16.9 points, 4.9 assists, and shooting 47.4 percent from the field through 29 appearances.