Moutinho arrived at Wolves following their return to the top flight in 2018 - and enjoyed five largely successful years at Molineux.
He was named player of the season in his first campaign and was even present alongside Ruben Neves in midfield for much of his time at the club.
The club have opted against offering Moutinho, along with Costa, who arrived at Molineux following an injury to summer signing Sasa Kalajdzic and went on to play 25 times last season, new deals.
Confirming the departures, sporting director Matt Hobbs paid tribute to Moutinho and insisted he will go down as one of the club's best ever players.
He said: "Joao’s going to go down as one of the best players to ever pull on the old gold, in my opinion. He was an integral part of the team the entire time he was here. 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.
“Everything he does is meticulous. He’s shown a lot of the younger players what you have to do to look after yourself and have a good career in the game. When he first came to the club, he was a big part of the culture change, because of his work ethic and how he managed himself before and after training. He definitely raised the levels and expectations amongst the players themselves.
“When he came in, we had a huge Portuguese contingent, and he was a hero to a lot of the guys for what he’d achieved in both club and international football. He just had that presence and people wanted to follow what he was he doing. We thank Joao for all he did at Wolves and wish him the best of luck for the future.”
On Costa, Hobbs added: "It feels the natural time to part ways because he was on a one-year contract. There was some internal conversations and we felt this was right.
"I’ve got no doubt that Diego will get another club off the back of his performances for sure. If a club calls me to ask about the person, he’ll get nothing but praise from me.”
Meanwhile, talks are underway with Traore over a potential new deal, however he is free to talk with other clubs - with Julen Lpetegui repeatedly saying the club were keen to keep hold of the winger.
"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," explained Hobbs.
"He’s probably earned the right to understand what else is out there.
“He’s a great guy around the place, always happy and friendly, so on every level we’d like to keep him. Sometimes it’s not possible, but we’ll certainly be trying. We hope we can come to an agreement but let’s see what happens over the next few weeks.”
Elsewhere, a number of youngsters have also been released, including Michael Agboola, Lee Harkin, Jack Hodnett, Luke Matheson, Taylor Perry and Jack Scott.