Ten Doeschate, 35, steps up from one-day captain to replace James Foster, who held the role for five years.
England all-rounder Bopara, 30, has been with Essex since 2002.
“I personally think Ryan will make a really good four-day captain. I believe he has the skills and determination to drive us forward,” head coach Chris Silverwood told BBC Essex.
All-rounder ten Doeschate, who has been with Essex since 2003 has scored 7,638 first-class runs at an average of 47.14 and taken 195 wickets, as well as appearing 33 one-day internationals and nine 20 matches for the Netherlands
“We’ve seen he’s a cool head out on the field and tactically he’s very good,” said Silverwood.
“That’s the sort of quality we need if we’re looking at not just getting out of Division Two, but competing in Division One and ultimately winning Division One, and I think he’s got the skills to take us there.”
Meanwhile, Bopara, whose last England appearance was in a one-day international against Afghanistan in March last year, is expected to try to play in the Indian Premier League this year, but this will not have a major impact on his Essex role.
Silverwood added: “Ravi wants to be a captain. He’s reached the stage of his life where he wants to be a leader on the field and that’s exactly what he’s going to get the opportunity to do.
“He is [putting himself up for IPL auction], there’s a possibility he’ll miss a couple of games but we’ve go to live with that – that’s the modern age of cricket.”