Viney joins the club on a two-season deal while Rivers has locked in for five.
“Once it became clear Jack was potentially available we were keen to add his experience and leadership to our playing group and we’re excited he is joining our club,” Head of List Management and Recruiting Matt Clarke said.
“Jack’s reputation across the competition is as a person of the highest character who leads by example with his uncompromising standards and drive to be successful.
“He was a key part of a premiership team at Melbourne, and we believe he can have a significant and positive impact on our midfield mix and developing group on and off the field.
“We look forward to welcoming Jack, Charlotte and their three daughters – Mila, Chloe and Ella – to West Coast.”
He added he was hopeful Rivers could add to both sides of the clubs’ game.
“Trent is a player we have tracked for some time, and we’re excited he has joined our club,” Clarke said.
“He has shown at Melbourne he is a defender who can attack the game from half-back and he also has the versatility to play through the midfield.
“Trent adds more premiership experience to our squad and is in the right age demographic to contribute to our list for years to come.”