Anscombe is grateful for the faith the defending champions have shown in him and New Zealand's Investec Super Rugby top point scorer has excelled in the Chiefs environment.
The first-five, who has spent much of the season playing out of position at fullback, is delighted to have been offered a contract.
"I am enjoying the culture and the challenging environment which I believed has helped grow my game and my confidence," he says.
The Chiefs snapped up former New Zealand under-20s hooker Marshall and identified the 20-year-old as being a player with great potential.
Due to injury, Marshall was given his first start before playing any ITM Cup matches and he has revelled in the game time he has received this year.
The Chiefs play the Hurricanes tonight at Waikato Stadium.