The move clears salary cap space for the Oilers.
Yamamoto had 10 goals and 15 assists in 58 games last season, which was his sixth in Edmonton. The 2017 first-round draft pick has one year remaining on his contract at $3.1 million.
Kostin, a restricted free agent, had 11 goals and 10 assists in 57 games with the Oilers after arriving from St. Louis in an October trade.
The Red Wings used its first pick in this week’s NHL draft on forward Nate Danielson at No. 9 overall.
Source: Yahoo Sports