Nivins attended County Prep High School(New Jersey) where he began as a baseball player before switching to basketball on his first year. In his Junior year he transferred to St. Anthony's High school (New Jersey). As a Senior, he averaged 15 points, 10 rebounds and five blocks and He helped the team to a 30-0 record and the school's ninth Tournament of Champions title in 2003-04.
Nivins attended Saint Joseph's University. He is the school's leader in career field goal percentage (63.4) and also one of 26 Hawks to record 1,000 points and 500 rebounds in his career. Nivins is fifth on SJU's all-time list with 110 blocks.
As a senior, he averaged a double-double (19.2 points, 11.8 rebounds) and nationally, he ranked fourth in rebounds per game behind John Bryant, Blake Griffin and Kenneth Faried.
Nivins was the 2009 Atlantic-10 Player of the Year and 2009 Big 5 Player of the Year.
After being selected by the Dallas Mavericks with the 56th overall pick of the 2009 NBA draft, on August 6, 2009, he signed for Bàsquet Manresa in the Spanish ACB.
On January 4, 2011, he signed with Belgian team Dexia Mons-Hainaut. On December 10, his draft rights were traded to the New York Knicks, along with the draft rights to Giorgos Printezis and Tyson Chandler in a three-way trade. The Mavericks received Andy Rautins from the Knicks and a second round pick from the Washington Wizards. The Wizards received Ronny Turiaf from the Knicks in addition to a Dallas 2012 second round pick, and 2013 Knicks second round pick, and cash considerations.
On August 20, 2012, Nivins moved to the French league, signing with Poitiers Basket 86 after averaging 10.4 points and 4.7 rebounds in 2011-12 in Belgium.
On June 21, 2013, Nivins signed with Élan Béarnais Pau-Orthez after averaging 14.4 points and 6.2 rebounds per game with Poitiers.
On June 3, 2014, Nivins signed with ASVEL Basket after averaging 15.5 points and 6.3 rebounds with Pau-Orthez.
On June 14, 2016, Nivins signed with Orléans Loiret Basket. On March 20, 2017, he parted ways with Orléans.
Nivins' father, Larry, played basketball at Slippery Rock University. Nivins majored in Sociology.