The teams announced the trade Tuesday night. Seattle general manager Jerry Dipoto said Scribner will compete for a spot in the bullpen.
Scribner, 30, appeared in a career-high 54 games last season for the A’s. He struck out 64 batters and walked just four in 60 innings of relief. But Scribner also gave up 14 home runs — the most of any reliever in baseball — and allowed 29 earned runs.
Scribner missed the final month of the season with a muscle strain.
Cochran-Gill turns 23 this month and appeared in 45 games between Single-A Bakersfield, Double-A Jackson and Triple-A Tacoma last season. He was originally a 17th round pick in the 2014 draft out of Auburn.