"I am thrilled to sign on for another year," said the 29-year-old, the first Welshman to captain a Super Rugby outfit.
"I believe this club is moving in the right direction and now I can continue to be a part of that.
"There was always an element of risk associated with the move, but I have thoroughly enjoyed my time in Melbourne.
"From a rugby perspective, playing against the world's best week in and week out has been great for the development of my game.
"It was always going to be a massive challenge, but I am very happy I came to Australia to play in this competition.
"On a personal note, I am thrilled to be staying in Melbourne, I have become very attached to this city over the past two years and it certainly feels like home now."
Delve, who was born in Cardiff, has previously enjoyed stints at Bath and Gloucester. He was part of the 2008 Grand Slam and joined the Wales squad for the three-Test tour of Australia following Toby Faletau's injury.
He did not add to his 11 Welsh caps but featured in the mid-week victory over ACT Brumbies.