The 24-year-old Wellman has two goals and five assists in 14 games with the Wild this season. He has spent most of his time this year with the AHL affiliate in Houston, where he had 13 goals and 11 assists in 25 games.
Christensen should help the Wild's depth at center. The 28-year-old has one goal and four assists in 20 games with the Rangers. His best season came with Pittsburgh in 2006-07, when he scored 18 goals.
The conditional draft choice the Wild will receive is in 2013.
The Wild also reassigned forward Chad Rau to Houston.
Minnesota announced the deal on Friday.