White revealed the information Wednesday to USA Today.
Carwin and Nelson will appear opposite one another on season 16 of the series, which is expected to begin during the fall. The show airs on FX.
"These two have been going at it on social media for a while and don't seem to like each other very much, but they are going to be seeing a lot of each other during this series," White told the newspaper.
Both Carwin and Nelson are former heavyweight titleholders.
Carwin claimed the UFC interim championship on March 27, 2010, with a first-round TKO of Frank Mir.
He relinquished the title in July 2010, falling victim to a second-round arm-triangle choke during a unification title bout with Brock Lesnar.
Carwin suffered his second loss in a row on June 11, 2011, when he came out on the short end of a unanimous decision to Junior dos Santos in a lopsided contest.
Later that year, Carwin (12-2) suffered a back injury while training. He underwent surgery to repair the problem.
Nelson was the 2009 TUF heavyweight winner -- knocking out Brendan Schaub in the first round on Dec. 5 of that year.
He has since gone 3-3 inside the Octagon, but looked impressive during his most recent outing. Nelson knocked out Dave Herman in 51 seconds on May 26.
The former International Fight League heavyweight champion has a professional record of 17-7.