The deal is worth $20.2 million over four years, ESPN's Marc Stein reported.
Ajinca, 27, joined the Pelicans in 2013 after two years away from the NBA. Last season, he played in 68 regular season games, making eight starts. Ajinca averaged 6.5 points, 4.6 rebounds and 0.8 blocks in 14.1 minutes per game in 2014-15.
Ajinca began his career in Charlotte and made stops in Dallas and Toronto before playing in Europe for two years. The Frenchman then signed with the Pelicans ahead of the 2013-14 season.
Earlier on Wednesday, the Pelicans signed forward Anthony Davis to a five-year, $145 million extension.
- Stanley Kay