Nikitin, 28, then agreed to a two-year contract with the Oilers; media reports indicate the deal is worth $9 million, with an average annual value of $4.5 million.
He had two goals and 15 points in 66 regular-season games for the Blue Jackets and was scoreless in five Stanley Cup Playoff games.
A fifth-round pick (No. 136) of the St. Louis Blues in the 2004 NHL Draft, Nikitin has 13 goals and 65 points in 206 games with the Blues and Blue Jackets.
Columbus will receive pick No. 137, which originally belonged to the Blue Jackets but was traded to the Oilers for defenseman Nick Schultz at the NHL Trade Deadline in March.