Wolves finished 13th this season after a turbulent campaign that saw Julen Lopetegui take charge in early November.
Moutinho joined Wolves from Monaco in 2018 and the Portugal international has made over 200 appearances for the Midlands club.
"Our success over the last four or five years, he’s been instrumental in. So, he now departs with nothing but thanks from the football club," Wolves sporting director Matt Hobbs said in a statement.
Costa signed in September amid an injury crisis and scored one goal in 25 games.
Traore made his 194th appearance in the final game of the season at Arsenal at the end of the five-year contract he signed on joining from Middlesbrough in the same year as Moutinho.
However, the Spain international could still be part of Lopetegui's plans next season.
"Adama is a player we’d like to keep, and we’re still talking to him. He’s now out of contract, but it doesn’t mean there’s not an opportunity to still come to an agreement, so conversations will be ongoing," Hobbs said.